TY - JOUR AB - Motivated by the recent preprint [\emph{arXiv:2004.08412}] by Ayala, Carinci, and Redig, we first provide a general framework for the study of scaling limits of higher-order fields. Then, by considering the same class of infinite interacting particle systems as in [\emph{arXiv:2004.08412}], namely symmetric simple exclusion and inclusion processes in the d-dimensional Euclidean lattice, we prove the hydrodynamic limit, and convergence for the equilibrium fluctuations, of higher-order fields. In particular, the limit fields exhibit a tensor structure. Our fluctuation result differs from that in [\emph{arXiv:2004.08412}], since we considered-dimensional Euclidean lattice, we prove the hydrodynamic limit, and convergence for the equilibrium fluctuations, of higher-order fields. In particular, the limit fields exhibit a tensor structure. Our fluctuation result differs from that in [\emph{arXiv:2004.08412}], since we consider a different notion of higher-order fluctuation fields. AU - Chen, Joe P. AU - Sau, Federico ID - 10613 IS - 3 JF - Markov Processes And Related Fields KW - interacting particle systems KW - higher-order fields KW - hydrodynamic limit KW - equilibrium fluctuations KW - duality SN - 1024-2953 TI - Higher-order hydrodynamics and equilibrium fluctuations of interacting particle systems VL - 27 ER - TY - JOUR AB - In this article we introduce a complete gradient estimate for symmetric quantum Markov semigroups on von Neumann algebras equipped with a normal faithful tracial state, which implies semi-convexity of the entropy with respect to the recently introduced noncommutative 2-Wasserstein distance. We show that this complete gradient estimate is stable under tensor products and free products and establish its validity for a number of examples. As an application we prove a complete modified logarithmic Sobolev inequality with optimal constant for Poisson-type semigroups on free group factors. AU - Wirth, Melchior AU - Zhang, Haonan ID - 9973 JF - Communications in Mathematical Physics KW - Mathematical Physics KW - Statistical and Nonlinear Physics SN - 0010-3616 TI - Complete gradient estimates of quantum Markov semigroups VL - 387 ER - TY - JOUR AB - In this paper, we introduce a random environment for the exclusion process in obtained by assigning a maximal occupancy to each site. This maximal occupancy is allowed to randomly vary among sites, and partial exclusion occurs. Under the assumption of ergodicity under translation and uniform ellipticity of the environment, we derive a quenched hydrodynamic limit in path space by strengthening the mild solution approach initiated in Nagy (2002) and Faggionato (2007). To this purpose, we prove, employing the technology developed for the random conductance model, a homogenization result in the form of an arbitrary starting point quenched invariance principle for a single particle in the same environment, which is a result of independent interest. The self-duality property of the partial exclusion process allows us to transfer this homogenization result to the particle system and, then, apply the tightness criterion in Redig et al. (2020). AU - Floreani, Simone AU - Redig, Frank AU - Sau, Federico ID - 10024 JF - Stochastic Processes and their Applications KW - hydrodynamic limit KW - random environment KW - random conductance model KW - arbitrary starting point quenched invariance principle KW - duality KW - mild solution SN - 0304-4149 TI - Hydrodynamics for the partial exclusion process in random environment VL - 142 ER - TY - JOUR AB - We extensively discuss the Rademacher and Sobolev-to-Lipschitz properties for generalized intrinsic distances on strongly local Dirichlet spaces possibly without square field operator. We present many non-smooth and infinite-dimensional examples. As an application, we prove the integral Varadhan short-time asymptotic with respect to a given distance function for a large class of strongly local Dirichlet forms. AU - Dello Schiavo, Lorenzo AU - Suzuki, Kohei ID - 10070 IS - 11 JF - Journal of Functional Analysis SN - 0022-1236 TI - Rademacher-type theorems and Sobolev-to-Lipschitz properties for strongly local Dirichlet spaces VL - 281 ER - TY - JOUR AB - We compute the deficiency spaces of operators of the form 𝐻𝐴⊗̂ 𝐼+𝐼⊗̂ 𝐻𝐵, for symmetric 𝐻𝐴 and self-adjoint 𝐻𝐵. This enables us to construct self-adjoint extensions (if they exist) by means of von Neumann's theory. The structure of the deficiency spaces for this case was asserted already in Ibort et al. [Boundary dynamics driven entanglement, J. Phys. A: Math. Theor. 47(38) (2014) 385301], but only proven under the restriction of 𝐻𝐵 having discrete, non-degenerate spectrum. AU - Lenz, Daniel AU - Weinmann, Timon AU - Wirth, Melchior ID - 9627 IS - 3 JF - Proceedings of the Edinburgh Mathematical Society SN - 0013-0915 TI - Self-adjoint extensions of bipartite Hamiltonians VL - 64 ER -