[{"oa_version":"Published Version","date_updated":"2024-02-05T13:04:23Z","date_created":"2024-02-04T23:00:54Z","author":[{"full_name":"Dello Schiavo, Lorenzo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","orcid":"0000-0002-9881-6870","first_name":"Lorenzo","last_name":"Dello Schiavo"},{"first_name":"Eva","last_name":"Kopfer","full_name":"Kopfer, Eva"},{"full_name":"Sturm, Karl Theodor","last_name":"Sturm","first_name":"Karl Theodor"}],"department":[{"_id":"JaMa"}],"publisher":"Springer Nature","publication_status":"epub_ahead","status":"public","title":"A discovery tour in random Riemannian geometry","_id":"14934","acknowledgement":"The authors would like to thank Matthias Erbar and Ronan Herry for valuable discussions on this project. They are also grateful to Nathanaël Berestycki, and Fabrice Baudoin for respectively pointing out the references [7], and [6, 24], and to Julien Fageot and Thomas Letendre for pointing out a mistake in a previous version of the proof of Proposition 3.10. The authors feel very much indebted to an anonymous reviewer for his/her careful reading and the many valuable suggestions that have significantly contributed to the improvement of the paper. L.D.S. gratefully acknowledges financial support by the Deutsche Forschungsgemeinschaft through CRC 1060 as well as through SPP 2265, and by the Austrian Science Fund (FWF) grant F65 at Institute of Science and Technology Austria. This research was funded in whole or in part by the Austrian Science Fund (FWF) ESPRIT 208. For the purpose of open access, the authors have applied a CC BY public copyright licence to any Author Accepted Manuscript version arising from this submission. E.K. and K.-T.S. gratefully acknowledge funding by the Deutsche Forschungsgemeinschaft through the Hausdorff Center for Mathematics and through CRC 1060 as well as through SPP 2265.\r\nOpen Access funding enabled and organized by Projekt DEAL.","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2024","abstract":[{"text":"We study random perturbations of a Riemannian manifold (M, g) by means of so-called\r\nFractional Gaussian Fields, which are defined intrinsically by the given manifold. The fields\r\nh• : ω \u0002→ hω will act on the manifold via the conformal transformation g \u0002→ gω := e2hω g.\r\nOur focus will be on the regular case with Hurst parameter H > 0, the critical case H = 0\r\nbeing the celebrated Liouville geometry in two dimensions. We want to understand how basic\r\ngeometric and functional-analytic quantities like diameter, volume, heat kernel, Brownian\r\nmotion, spectral bound, or spectral gap change under the influence of the noise. And if so, is\r\nit possible to quantify these dependencies in terms of key parameters of the noise? Another\r\ngoal is to define and analyze in detail the Fractional Gaussian Fields on a general Riemannian\r\nmanifold, a fascinating object of independent interest.","lang":"eng"}],"type":"journal_article","language":[{"iso":"eng"}],"doi":"10.1007/s11118-023-10118-0","date_published":"2024-01-26T00:00:00Z","project":[{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems"}],"article_type":"original","quality_controlled":"1","oa":1,"main_file_link":[{"open_access":"1","url":"https://doi.org/10.1007/s11118-023-10118-0"}],"citation":{"chicago":"Dello Schiavo, Lorenzo, Eva Kopfer, and Karl Theodor Sturm. “A Discovery Tour in Random Riemannian Geometry.” Potential Analysis. Springer Nature, 2024. https://doi.org/10.1007/s11118-023-10118-0.","short":"L. Dello Schiavo, E. Kopfer, K.T. Sturm, Potential Analysis (2024).","mla":"Dello Schiavo, Lorenzo, et al. “A Discovery Tour in Random Riemannian Geometry.” Potential Analysis, Springer Nature, 2024, doi:10.1007/s11118-023-10118-0.","apa":"Dello Schiavo, L., Kopfer, E., & Sturm, K. T. (2024). A discovery tour in random Riemannian geometry. Potential Analysis. Springer Nature. https://doi.org/10.1007/s11118-023-10118-0","ieee":"L. Dello Schiavo, E. Kopfer, and K. T. Sturm, “A discovery tour in random Riemannian geometry,” Potential Analysis. Springer Nature, 2024.","ista":"Dello Schiavo L, Kopfer E, Sturm KT. 2024. A discovery tour in random Riemannian geometry. Potential Analysis.","ama":"Dello Schiavo L, Kopfer E, Sturm KT. A discovery tour in random Riemannian geometry. Potential Analysis. 2024. doi:10.1007/s11118-023-10118-0"},"publication":"Potential Analysis","article_processing_charge":"Yes (via OA deal)","publication_identifier":{"issn":["0926-2601"],"eissn":["1572-929X"]},"day":"26","month":"01","scopus_import":"1"},{"article_type":"original","publication":"Journal of Evolution Equations","citation":{"chicago":"Dello Schiavo, Lorenzo, and Melchior Wirth. “Ergodic Decompositions of Dirichlet Forms under Order Isomorphisms.” Journal of Evolution Equations. Springer Nature, 2023. https://doi.org/10.1007/s00028-022-00859-7.","short":"L. Dello Schiavo, M. Wirth, Journal of Evolution Equations 23 (2023).","mla":"Dello Schiavo, Lorenzo, and Melchior Wirth. “Ergodic Decompositions of Dirichlet Forms under Order Isomorphisms.” Journal of Evolution Equations, vol. 23, no. 1, 9, Springer Nature, 2023, doi:10.1007/s00028-022-00859-7.","ieee":"L. Dello Schiavo and M. Wirth, “Ergodic decompositions of Dirichlet forms under order isomorphisms,” Journal of Evolution Equations, vol. 23, no. 1. Springer Nature, 2023.","apa":"Dello Schiavo, L., & Wirth, M. (2023). Ergodic decompositions of Dirichlet forms under order isomorphisms. Journal of Evolution Equations. Springer Nature. https://doi.org/10.1007/s00028-022-00859-7","ista":"Dello Schiavo L, Wirth M. 2023. Ergodic decompositions of Dirichlet forms under order isomorphisms. Journal of Evolution Equations. 23(1), 9.","ama":"Dello Schiavo L, Wirth M. Ergodic decompositions of Dirichlet forms under order isomorphisms. Journal of Evolution Equations. 2023;23(1). doi:10.1007/s00028-022-00859-7"},"date_published":"2023-01-01T00:00:00Z","scopus_import":"1","day":"01","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","status":"public","title":"Ergodic decompositions of Dirichlet forms under order isomorphisms","ddc":["510"],"intvolume":" 23","_id":"12104","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Published Version","file":[{"creator":"dernst","file_size":422612,"content_type":"application/pdf","file_name":"2023_JourEvolutionEquations_DelloSchiavo.pdf","access_level":"open_access","date_created":"2023-01-20T10:45:06Z","date_updated":"2023-01-20T10:45:06Z","success":1,"checksum":"1f34f3e2cb521033de6154f274ea3a4e","file_id":"12325","relation":"main_file"}],"type":"journal_article","abstract":[{"lang":"eng","text":"We study ergodic decompositions of Dirichlet spaces under intertwining via unitary order isomorphisms. We show that the ergodic decomposition of a quasi-regular Dirichlet space is unique up to a unique isomorphism of the indexing space. Furthermore, every unitary order isomorphism intertwining two quasi-regular Dirichlet spaces is decomposable over their ergodic decompositions up to conjugation via an isomorphism of the corresponding indexing spaces."}],"issue":"1","quality_controlled":"1","isi":1,"project":[{"name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504"},{"call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425"},{"name":"Configuration Spaces over Non-Smooth Spaces","_id":"34dbf174-11ca-11ed-8bc3-afe9d43d4b9c","grant_number":"E208"},{"grant_number":"ESP156_N","_id":"34c6ea2d-11ca-11ed-8bc3-c04f3c502833","name":"Gradient flow techniques for quantum Markov semigroups"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"external_id":{"isi":["000906214600004"]},"language":[{"iso":"eng"}],"doi":"10.1007/s00028-022-00859-7","month":"01","publication_identifier":{"issn":["1424-3199"],"eissn":["1424-3202"]},"publication_status":"published","publisher":"Springer Nature","department":[{"_id":"JaMa"}],"year":"2023","acknowledgement":"Research supported by the Austrian Science Fund (FWF) grant F65 at the Institute of Science and Technology Austria and by the European Research Council (ERC) (Grant agreement No. 716117 awarded to Prof. Dr. Jan Maas). L.D.S. gratefully acknowledges funding of his current position by the Austrian Science Fund (FWF) through the ESPRIT Programme (Grant No. 208). M.W. gratefully acknowledges funding of his current position by the Austrian Science Fund (FWF) through the ESPRIT Programme (Grant No. 156).","date_created":"2023-01-08T23:00:53Z","date_updated":"2023-06-28T11:54:35Z","volume":23,"author":[{"full_name":"Dello Schiavo, Lorenzo","last_name":"Dello Schiavo","first_name":"Lorenzo","orcid":"0000-0002-9881-6870","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E"},{"last_name":"Wirth","first_name":"Melchior","orcid":"0000-0002-0519-4241","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","full_name":"Wirth, Melchior"}],"article_number":"9","license":"https://creativecommons.org/licenses/by/4.0/","file_date_updated":"2023-01-20T10:45:06Z","ec_funded":1},{"page":"717-750","article_type":"original","citation":{"short":"M. Wirth, H. Zhang, Annales Henri Poincare 24 (2023) 717–750.","mla":"Wirth, Melchior, and Haonan Zhang. “Curvature-Dimension Conditions for Symmetric Quantum Markov Semigroups.” Annales Henri Poincare, vol. 24, Springer Nature, 2023, pp. 717–50, doi:10.1007/s00023-022-01220-x.","chicago":"Wirth, Melchior, and Haonan Zhang. “Curvature-Dimension Conditions for Symmetric Quantum Markov Semigroups.” Annales Henri Poincare. Springer Nature, 2023. https://doi.org/10.1007/s00023-022-01220-x.","ama":"Wirth M, Zhang H. Curvature-dimension conditions for symmetric quantum Markov semigroups. Annales Henri Poincare. 2023;24:717-750. doi:10.1007/s00023-022-01220-x","apa":"Wirth, M., & Zhang, H. (2023). Curvature-dimension conditions for symmetric quantum Markov semigroups. Annales Henri Poincare. Springer Nature. https://doi.org/10.1007/s00023-022-01220-x","ieee":"M. Wirth and H. Zhang, “Curvature-dimension conditions for symmetric quantum Markov semigroups,” Annales Henri Poincare, vol. 24. Springer Nature, pp. 717–750, 2023.","ista":"Wirth M, Zhang H. 2023. Curvature-dimension conditions for symmetric quantum Markov semigroups. Annales Henri Poincare. 24, 717–750."},"publication":"Annales Henri Poincare","date_published":"2023-03-01T00:00:00Z","scopus_import":"1","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","day":"01","intvolume":" 24","ddc":["510"],"title":"Curvature-dimension conditions for symmetric quantum Markov semigroups","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"12087","oa_version":"Published Version","file":[{"creator":"dernst","file_size":554871,"content_type":"application/pdf","file_name":"2023_AnnalesHenriPoincare_Wirth.pdf","access_level":"open_access","date_created":"2023-08-14T11:38:28Z","date_updated":"2023-08-14T11:38:28Z","success":1,"checksum":"8c7b185eba5ccd92ef55c120f654222c","file_id":"14051","relation":"main_file"}],"type":"journal_article","abstract":[{"lang":"eng","text":"Following up on the recent work on lower Ricci curvature bounds for quantum systems, we introduce two noncommutative versions of curvature-dimension bounds for symmetric quantum Markov semigroups over matrix algebras. Under suitable such curvature-dimension conditions, we prove a family of dimension-dependent functional inequalities, a version of the Bonnet–Myers theorem and concavity of entropy power in the noncommutative setting. We also provide examples satisfying certain curvature-dimension conditions, including Schur multipliers over matrix algebras, Herz–Schur multipliers over group algebras and generalized depolarizing semigroups."}],"project":[{"call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425"},{"name":"Curvature-dimension in noncommutative analysis","grant_number":"M03337","_id":"eb958bca-77a9-11ec-83b8-c565cb50d8d6"},{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117","call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics"},{"name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"}],"quality_controlled":"1","isi":1,"oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"arxiv":["2105.08303"],"isi":["000837499800002"]},"language":[{"iso":"eng"}],"doi":"10.1007/s00023-022-01220-x","publication_identifier":{"issn":["1424-0637"]},"month":"03","publisher":"Springer Nature","department":[{"_id":"JaMa"}],"publication_status":"published","acknowledgement":"H.Z. is supported by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411 and the Lise Meitner fellowship, Austrian Science Fund (FWF) M3337. M.W. acknowledges support from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 716117) and from the Austrian Science Fund (FWF) through grant number F65. Both authors would like to thank Jan Maas for fruitful discussions and helpful comments. Open access funding provided by Austrian Science Fund (FWF).","year":"2023","volume":24,"date_updated":"2023-08-14T11:39:28Z","date_created":"2022-09-11T22:01:57Z","author":[{"full_name":"Wirth, Melchior","first_name":"Melchior","last_name":"Wirth","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","orcid":"0000-0002-0519-4241"},{"last_name":"Zhang","first_name":"Haonan","id":"D8F41E38-9E66-11E9-A9E2-65C2E5697425","full_name":"Zhang, Haonan"}],"ec_funded":1,"file_date_updated":"2023-08-14T11:38:28Z"},{"scopus_import":"1","day":"01","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","article_type":"original","page":"573-615","publication":"Potential Analysis","citation":{"short":"L. Dello Schiavo, Potential Analysis 58 (2023) 573–615.","mla":"Dello Schiavo, Lorenzo. “Ergodic Decomposition of Dirichlet Forms via Direct Integrals and Applications.” Potential Analysis, vol. 58, Springer Nature, 2023, pp. 573–615, doi:10.1007/s11118-021-09951-y.","chicago":"Dello Schiavo, Lorenzo. “Ergodic Decomposition of Dirichlet Forms via Direct Integrals and Applications.” Potential Analysis. Springer Nature, 2023. https://doi.org/10.1007/s11118-021-09951-y.","ama":"Dello Schiavo L. Ergodic decomposition of Dirichlet forms via direct integrals and applications. Potential Analysis. 2023;58:573-615. doi:10.1007/s11118-021-09951-y","apa":"Dello Schiavo, L. (2023). Ergodic decomposition of Dirichlet forms via direct integrals and applications. Potential Analysis. Springer Nature. https://doi.org/10.1007/s11118-021-09951-y","ieee":"L. Dello Schiavo, “Ergodic decomposition of Dirichlet forms via direct integrals and applications,” Potential Analysis, vol. 58. Springer Nature, pp. 573–615, 2023.","ista":"Dello Schiavo L. 2023. Ergodic decomposition of Dirichlet forms via direct integrals and applications. Potential Analysis. 58, 573–615."},"date_published":"2023-03-01T00:00:00Z","type":"journal_article","abstract":[{"text":"We study direct integrals of quadratic and Dirichlet forms. We show that each quasi-regular Dirichlet space over a probability space admits a unique representation as a direct integral of irreducible Dirichlet spaces, quasi-regular for the same underlying topology. The same holds for each quasi-regular strongly local Dirichlet space over a metrizable Luzin σ-finite Radon measure space, and admitting carré du champ operator. In this case, the representation is only projectively unique.","lang":"eng"}],"title":"Ergodic decomposition of Dirichlet forms via direct integrals and applications","status":"public","ddc":["510"],"intvolume":" 58","_id":"10145","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Published Version","file":[{"checksum":"625526482be300ca7281c91c30d41725","success":1,"date_created":"2023-10-04T09:18:59Z","date_updated":"2023-10-04T09:18:59Z","relation":"main_file","file_id":"14387","content_type":"application/pdf","file_size":806391,"creator":"dernst","access_level":"open_access","file_name":"2023_PotentialAnalysis_DelloSchiavo.pdf"}],"month":"03","publication_identifier":{"issn":["0926-2601"],"eissn":["1572-929X"]},"quality_controlled":"1","isi":1,"project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"},{"name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504"},{"grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"external_id":{"arxiv":["2003.01366"],"isi":["000704213400001"]},"language":[{"iso":"eng"}],"doi":"10.1007/s11118-021-09951-y","file_date_updated":"2023-10-04T09:18:59Z","ec_funded":1,"publication_status":"published","department":[{"_id":"JaMa"}],"publisher":"Springer Nature","acknowledgement":"The author is grateful to Professors Sergio Albeverio and Andreas Eberle, and to Dr. Kohei Suzuki, for fruitful conversations on the subject of the present work, and for respectively pointing out the references [1, 13], and [3, 20]. Finally, he is especially grateful to an anonymous Reviewer for their very careful reading and their suggestions which improved the readability of the paper.","year":"2023","date_updated":"2023-10-04T09:19:12Z","date_created":"2021-10-17T22:01:17Z","volume":58,"author":[{"full_name":"Dello Schiavo, Lorenzo","first_name":"Lorenzo","last_name":"Dello Schiavo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","orcid":"0000-0002-9881-6870"}]},{"abstract":[{"text":"This paper deals with the large-scale behaviour of dynamical optimal transport on Zd\r\n-periodic graphs with general lower semicontinuous and convex energy densities. Our main contribution is a homogenisation result that describes the effective behaviour of the discrete problems in terms of a continuous optimal transport problem. The effective energy density can be explicitly expressed in terms of a cell formula, which is a finite-dimensional convex programming problem that depends non-trivially on the local geometry of the discrete graph and the discrete energy density. Our homogenisation result is derived from a Γ\r\n-convergence result for action functionals on curves of measures, which we prove under very mild growth conditions on the energy density. We investigate the cell formula in several cases of interest, including finite-volume discretisations of the Wasserstein distance, where non-trivial limiting behaviour occurs.","lang":"eng"}],"issue":"5","type":"journal_article","oa_version":"Published Version","file":[{"creator":"dernst","file_size":1240995,"content_type":"application/pdf","file_name":"2023_CalculusEquations_Gladbach.pdf","access_level":"open_access","date_updated":"2023-10-04T11:34:10Z","date_created":"2023-10-04T11:34:10Z","success":1,"checksum":"359bee38d94b7e0aa73925063cb8884d","file_id":"14393","relation":"main_file"}],"_id":"12959","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","ddc":["510"],"title":"Homogenisation of dynamical optimal transport on periodic graphs","intvolume":" 62","day":"28","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","scopus_import":"1","date_published":"2023-04-28T00:00:00Z","publication":"Calculus of Variations and Partial Differential Equations","citation":{"mla":"Gladbach, Peter, et al. “Homogenisation of Dynamical Optimal Transport on Periodic Graphs.” Calculus of Variations and Partial Differential Equations, vol. 62, no. 5, 143, Springer Nature, 2023, doi:10.1007/s00526-023-02472-z.","short":"P. Gladbach, E. Kopfer, J. Maas, L. Portinale, Calculus of Variations and Partial Differential Equations 62 (2023).","chicago":"Gladbach, Peter, Eva Kopfer, Jan Maas, and Lorenzo Portinale. “Homogenisation of Dynamical Optimal Transport on Periodic Graphs.” Calculus of Variations and Partial Differential Equations. Springer Nature, 2023. https://doi.org/10.1007/s00526-023-02472-z.","ama":"Gladbach P, Kopfer E, Maas J, Portinale L. Homogenisation of dynamical optimal transport on periodic graphs. Calculus of Variations and Partial Differential Equations. 2023;62(5). doi:10.1007/s00526-023-02472-z","ista":"Gladbach P, Kopfer E, Maas J, Portinale L. 2023. Homogenisation of dynamical optimal transport on periodic graphs. Calculus of Variations and Partial Differential Equations. 62(5), 143.","apa":"Gladbach, P., Kopfer, E., Maas, J., & Portinale, L. (2023). Homogenisation of dynamical optimal transport on periodic graphs. Calculus of Variations and Partial Differential Equations. Springer Nature. https://doi.org/10.1007/s00526-023-02472-z","ieee":"P. Gladbach, E. Kopfer, J. Maas, and L. Portinale, “Homogenisation of dynamical optimal transport on periodic graphs,” Calculus of Variations and Partial Differential Equations, vol. 62, no. 5. Springer Nature, 2023."},"article_type":"original","file_date_updated":"2023-10-04T11:34:10Z","ec_funded":1,"article_number":"143","author":[{"full_name":"Gladbach, Peter","last_name":"Gladbach","first_name":"Peter"},{"first_name":"Eva","last_name":"Kopfer","full_name":"Kopfer, Eva"},{"orcid":"0000-0002-0845-1338","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","last_name":"Maas","first_name":"Jan","full_name":"Maas, Jan"},{"first_name":"Lorenzo","last_name":"Portinale","id":"30AD2CBC-F248-11E8-B48F-1D18A9856A87","full_name":"Portinale, Lorenzo"}],"date_updated":"2023-10-04T11:34:49Z","date_created":"2023-05-14T22:01:00Z","volume":62,"year":"2023","acknowledgement":"J.M. gratefully acknowledges support by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 716117). J.M and L.P. also acknowledge support from the Austrian Science Fund (FWF), grants No F65 and W1245. E.K. gratefully acknowledges support by the German Research Foundation through the Hausdorff Center for Mathematics and the Collaborative Research Center 1060. P.G. is partially funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)—350398276. We thank the anonymous reviewer for the careful reading and for useful suggestions. Open access funding provided by Austrian Science Fund (FWF).","publication_status":"published","department":[{"_id":"JaMa"}],"publisher":"Springer Nature","month":"04","publication_identifier":{"issn":["0944-2669"],"eissn":["1432-0835"]},"doi":"10.1007/s00526-023-02472-z","language":[{"iso":"eng"}],"external_id":{"arxiv":["2110.15321"],"isi":["000980588900001"]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"quality_controlled":"1","isi":1,"project":[{"call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425"},{"name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504"},{"call_identifier":"FWF","name":"Dissipation and Dispersion in Nonlinear Partial Differential Equations","_id":"260788DE-B435-11E9-9278-68D0E5697425"}]}]