---
_id: '10862'
abstract:
- lang: eng
text: We consider the sum of two large Hermitian matrices A and B with a Haar unitary
conjugation bringing them into a general relative position. We prove that the
eigenvalue density on the scale slightly above the local eigenvalue spacing is
asymptotically given by the free additive convolution of the laws of A and B as
the dimension of the matrix increases. This implies optimal rigidity of the eigenvalues
and optimal rate of convergence in Voiculescu's theorem. Our previous works [4],
[5] established these results in the bulk spectrum, the current paper completely
settles the problem at the spectral edges provided they have the typical square-root
behavior. The key element of our proof is to compensate the deterioration of the
stability of the subordination equations by sharp error estimates that properly
account for the local density near the edge. Our results also hold if the Haar
unitary matrix is replaced by the Haar orthogonal matrix.
acknowledgement: Partially supported by ERC Advanced Grant RANMAT No. 338804.
article_number: '108639'
article_processing_charge: No
article_type: original
author:
- first_name: Zhigang
full_name: Bao, Zhigang
id: 442E6A6C-F248-11E8-B48F-1D18A9856A87
last_name: Bao
orcid: 0000-0003-3036-1475
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Kevin
full_name: Schnelli, Kevin
last_name: Schnelli
citation:
ama: Bao Z, Erdös L, Schnelli K. Spectral rigidity for addition of random matrices
at the regular edge. Journal of Functional Analysis. 2020;279(7). doi:10.1016/j.jfa.2020.108639
apa: Bao, Z., Erdös, L., & Schnelli, K. (2020). Spectral rigidity for addition
of random matrices at the regular edge. Journal of Functional Analysis.
Elsevier. https://doi.org/10.1016/j.jfa.2020.108639
chicago: Bao, Zhigang, László Erdös, and Kevin Schnelli. “Spectral Rigidity for
Addition of Random Matrices at the Regular Edge.” Journal of Functional Analysis.
Elsevier, 2020. https://doi.org/10.1016/j.jfa.2020.108639.
ieee: Z. Bao, L. Erdös, and K. Schnelli, “Spectral rigidity for addition of random
matrices at the regular edge,” Journal of Functional Analysis, vol. 279,
no. 7. Elsevier, 2020.
ista: Bao Z, Erdös L, Schnelli K. 2020. Spectral rigidity for addition of random
matrices at the regular edge. Journal of Functional Analysis. 279(7), 108639.
mla: Bao, Zhigang, et al. “Spectral Rigidity for Addition of Random Matrices at
the Regular Edge.” Journal of Functional Analysis, vol. 279, no. 7, 108639,
Elsevier, 2020, doi:10.1016/j.jfa.2020.108639.
short: Z. Bao, L. Erdös, K. Schnelli, Journal of Functional Analysis 279 (2020).
date_created: 2022-03-18T10:18:59Z
date_published: 2020-10-15T00:00:00Z
date_updated: 2023-08-24T14:08:42Z
day: '15'
department:
- _id: LaEr
doi: 10.1016/j.jfa.2020.108639
ec_funded: 1
external_id:
arxiv:
- '1708.01597'
isi:
- '000559623200009'
intvolume: ' 279'
isi: 1
issue: '7'
keyword:
- Analysis
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1708.01597
month: '10'
oa: 1
oa_version: Preprint
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication: Journal of Functional Analysis
publication_identifier:
issn:
- 0022-1236
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Spectral rigidity for addition of random matrices at the regular edge
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 279
year: '2020'
...
---
_id: '10867'
abstract:
- lang: eng
text: In this paper we find a tight estimate for Gromov’s waist of the balls in
spaces of constant curvature, deduce the estimates for the balls in Riemannian
manifolds with upper bounds on the curvature (CAT(ϰ)-spaces), and establish similar
result for normed spaces.
acknowledgement: ' Supported by the Russian Foundation for Basic Research grant 18-01-00036.'
article_processing_charge: No
article_type: original
author:
- first_name: Arseniy
full_name: Akopyan, Arseniy
id: 430D2C90-F248-11E8-B48F-1D18A9856A87
last_name: Akopyan
orcid: 0000-0002-2548-617X
- first_name: Roman
full_name: Karasev, Roman
last_name: Karasev
citation:
ama: Akopyan A, Karasev R. Waist of balls in hyperbolic and spherical spaces. International
Mathematics Research Notices. 2020;2020(3):669-697. doi:10.1093/imrn/rny037
apa: Akopyan, A., & Karasev, R. (2020). Waist of balls in hyperbolic and spherical
spaces. International Mathematics Research Notices. Oxford University Press.
https://doi.org/10.1093/imrn/rny037
chicago: Akopyan, Arseniy, and Roman Karasev. “Waist of Balls in Hyperbolic and
Spherical Spaces.” International Mathematics Research Notices. Oxford University
Press, 2020. https://doi.org/10.1093/imrn/rny037.
ieee: A. Akopyan and R. Karasev, “Waist of balls in hyperbolic and spherical spaces,”
International Mathematics Research Notices, vol. 2020, no. 3. Oxford University
Press, pp. 669–697, 2020.
ista: Akopyan A, Karasev R. 2020. Waist of balls in hyperbolic and spherical spaces.
International Mathematics Research Notices. 2020(3), 669–697.
mla: Akopyan, Arseniy, and Roman Karasev. “Waist of Balls in Hyperbolic and Spherical
Spaces.” International Mathematics Research Notices, vol. 2020, no. 3,
Oxford University Press, 2020, pp. 669–97, doi:10.1093/imrn/rny037.
short: A. Akopyan, R. Karasev, International Mathematics Research Notices 2020 (2020)
669–697.
date_created: 2022-03-18T11:39:30Z
date_published: 2020-02-01T00:00:00Z
date_updated: 2023-08-24T14:19:55Z
day: '01'
department:
- _id: HeEd
doi: 10.1093/imrn/rny037
external_id:
arxiv:
- '1702.07513'
isi:
- '000522852700002'
intvolume: ' 2020'
isi: 1
issue: '3'
keyword:
- General Mathematics
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1702.07513
month: '02'
oa: 1
oa_version: Preprint
page: 669-697
publication: International Mathematics Research Notices
publication_identifier:
eissn:
- 1687-0247
issn:
- 1073-7928
publication_status: published
publisher: Oxford University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Waist of balls in hyperbolic and spherical spaces
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 2020
year: '2020'
...
---
_id: '9799'
abstract:
- lang: eng
text: Fitness interactions between mutations can influence a population’s evolution
in many different ways. While epistatic effects are difficult to measure precisely,
important information is captured by the mean and variance of log fitnesses for
individuals carrying different numbers of mutations. We derive predictions for
these quantities from a class of simple fitness landscapes, based on models of
optimizing selection on quantitative traits. We also explore extensions to the
models, including modular pleiotropy, variable effect sizes, mutational bias and
maladaptation of the wild type. We illustrate our approach by reanalysing a large
dataset of mutant effects in a yeast snoRNA. Though characterized by some large
epistatic effects, these data give a good overall fit to the non-epistatic null
model, suggesting that epistasis might have limited influence on the evolutionary
dynamics in this system. We also show how the amount of epistasis depends on both
the underlying fitness landscape and the distribution of mutations, and so is
expected to vary in consistent ways between new mutations, standing variation
and fixed mutations.
article_processing_charge: No
author:
- first_name: Christelle
full_name: Fraisse, Christelle
id: 32DF5794-F248-11E8-B48F-1D18A9856A87
last_name: Fraisse
orcid: 0000-0001-8441-5075
- first_name: John J.
full_name: Welch, John J.
last_name: Welch
citation:
ama: Fraisse C, Welch JJ. Simulation code for Fig S1 from the distribution of epistasis
on simple fitness landscapes. 2020. doi:10.6084/m9.figshare.7957469.v1
apa: Fraisse, C., & Welch, J. J. (2020). Simulation code for Fig S1 from the
distribution of epistasis on simple fitness landscapes. Royal Society of London.
https://doi.org/10.6084/m9.figshare.7957469.v1
chicago: Fraisse, Christelle, and John J. Welch. “Simulation Code for Fig S1 from
the Distribution of Epistasis on Simple Fitness Landscapes.” Royal Society of
London, 2020. https://doi.org/10.6084/m9.figshare.7957469.v1.
ieee: C. Fraisse and J. J. Welch, “Simulation code for Fig S1 from the distribution
of epistasis on simple fitness landscapes.” Royal Society of London, 2020.
ista: Fraisse C, Welch JJ. 2020. Simulation code for Fig S1 from the distribution
of epistasis on simple fitness landscapes, Royal Society of London, 10.6084/m9.figshare.7957469.v1.
mla: Fraisse, Christelle, and John J. Welch. Simulation Code for Fig S1 from
the Distribution of Epistasis on Simple Fitness Landscapes. Royal Society
of London, 2020, doi:10.6084/m9.figshare.7957469.v1.
short: C. Fraisse, J.J. Welch, (2020).
date_created: 2021-08-06T11:26:57Z
date_published: 2020-10-15T00:00:00Z
date_updated: 2023-08-25T10:34:41Z
day: '15'
department:
- _id: BeVi
- _id: NiBa
doi: 10.6084/m9.figshare.7957469.v1
main_file_link:
- open_access: '1'
url: https://doi.org/10.6084/m9.figshare.7957469.v1
month: '10'
oa: 1
oa_version: Published Version
publisher: Royal Society of London
related_material:
record:
- id: '6467'
relation: used_in_publication
status: public
status: public
title: Simulation code for Fig S1 from the distribution of epistasis on simple fitness
landscapes
type: research_data_reference
user_id: 6785fbc1-c503-11eb-8a32-93094b40e1cf
year: '2020'
...
---
_id: '9798'
abstract:
- lang: eng
text: Fitness interactions between mutations can influence a population’s evolution
in many different ways. While epistatic effects are difficult to measure precisely,
important information is captured by the mean and variance of log fitnesses for
individuals carrying different numbers of mutations. We derive predictions for
these quantities from a class of simple fitness landscapes, based on models of
optimizing selection on quantitative traits. We also explore extensions to the
models, including modular pleiotropy, variable effect sizes, mutational bias and
maladaptation of the wild type. We illustrate our approach by reanalysing a large
dataset of mutant effects in a yeast snoRNA. Though characterized by some large
epistatic effects, these data give a good overall fit to the non-epistatic null
model, suggesting that epistasis might have limited influence on the evolutionary
dynamics in this system. We also show how the amount of epistasis depends on both
the underlying fitness landscape and the distribution of mutations, and so is
expected to vary in consistent ways between new mutations, standing variation
and fixed mutations.
article_processing_charge: No
author:
- first_name: Christelle
full_name: Fraisse, Christelle
id: 32DF5794-F248-11E8-B48F-1D18A9856A87
last_name: Fraisse
orcid: 0000-0001-8441-5075
- first_name: John J.
full_name: Welch, John J.
last_name: Welch
citation:
ama: Fraisse C, Welch JJ. Simulation code for Fig S2 from the distribution of epistasis
on simple fitness landscapes. 2020. doi:10.6084/m9.figshare.7957472.v1
apa: Fraisse, C., & Welch, J. J. (2020). Simulation code for Fig S2 from the
distribution of epistasis on simple fitness landscapes. Royal Society of London.
https://doi.org/10.6084/m9.figshare.7957472.v1
chicago: Fraisse, Christelle, and John J. Welch. “Simulation Code for Fig S2 from
the Distribution of Epistasis on Simple Fitness Landscapes.” Royal Society of
London, 2020. https://doi.org/10.6084/m9.figshare.7957472.v1.
ieee: C. Fraisse and J. J. Welch, “Simulation code for Fig S2 from the distribution
of epistasis on simple fitness landscapes.” Royal Society of London, 2020.
ista: Fraisse C, Welch JJ. 2020. Simulation code for Fig S2 from the distribution
of epistasis on simple fitness landscapes, Royal Society of London, 10.6084/m9.figshare.7957472.v1.
mla: Fraisse, Christelle, and John J. Welch. Simulation Code for Fig S2 from
the Distribution of Epistasis on Simple Fitness Landscapes. Royal Society
of London, 2020, doi:10.6084/m9.figshare.7957472.v1.
short: C. Fraisse, J.J. Welch, (2020).
date_created: 2021-08-06T11:18:15Z
date_published: 2020-10-15T00:00:00Z
date_updated: 2023-08-25T10:34:41Z
day: '15'
department:
- _id: BeVi
- _id: NiBa
doi: 10.6084/m9.figshare.7957472.v1
main_file_link:
- open_access: '1'
url: https://doi.org/10.6084/m9.figshare.7957472.v1
month: '10'
oa: 1
oa_version: Published Version
publisher: Royal Society of London
related_material:
record:
- id: '6467'
relation: used_in_publication
status: public
status: public
title: Simulation code for Fig S2 from the distribution of epistasis on simple fitness
landscapes
type: research_data_reference
user_id: 6785fbc1-c503-11eb-8a32-93094b40e1cf
year: '2020'
...
---
_id: '6488'
abstract:
- lang: eng
text: We prove a central limit theorem for the difference of linear eigenvalue statistics
of a sample covariance matrix W˜ and its minor W. We find that the fluctuation
of this difference is much smaller than those of the individual linear statistics,
as a consequence of the strong correlation between the eigenvalues of W˜ and W.
Our result identifies the fluctuation of the spatial derivative of the approximate
Gaussian field in the recent paper by Dumitru and Paquette. Unlike in a similar
result for Wigner matrices, for sample covariance matrices, the fluctuation may
entirely vanish.
article_number: '2050006'
article_processing_charge: No
article_type: original
author:
- first_name: Giorgio
full_name: Cipolloni, Giorgio
id: 42198EFA-F248-11E8-B48F-1D18A9856A87
last_name: Cipolloni
orcid: 0000-0002-4901-7992
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
citation:
ama: 'Cipolloni G, Erdös L. Fluctuations for differences of linear eigenvalue statistics
for sample covariance matrices. Random Matrices: Theory and Application.
2020;9(3). doi:10.1142/S2010326320500069'
apa: 'Cipolloni, G., & Erdös, L. (2020). Fluctuations for differences of linear
eigenvalue statistics for sample covariance matrices. Random Matrices: Theory
and Application. World Scientific Publishing. https://doi.org/10.1142/S2010326320500069'
chicago: 'Cipolloni, Giorgio, and László Erdös. “Fluctuations for Differences of
Linear Eigenvalue Statistics for Sample Covariance Matrices.” Random Matrices:
Theory and Application. World Scientific Publishing, 2020. https://doi.org/10.1142/S2010326320500069.'
ieee: 'G. Cipolloni and L. Erdös, “Fluctuations for differences of linear eigenvalue
statistics for sample covariance matrices,” Random Matrices: Theory and Application,
vol. 9, no. 3. World Scientific Publishing, 2020.'
ista: 'Cipolloni G, Erdös L. 2020. Fluctuations for differences of linear eigenvalue
statistics for sample covariance matrices. Random Matrices: Theory and Application.
9(3), 2050006.'
mla: 'Cipolloni, Giorgio, and László Erdös. “Fluctuations for Differences of Linear
Eigenvalue Statistics for Sample Covariance Matrices.” Random Matrices: Theory
and Application, vol. 9, no. 3, 2050006, World Scientific Publishing, 2020,
doi:10.1142/S2010326320500069.'
short: 'G. Cipolloni, L. Erdös, Random Matrices: Theory and Application 9 (2020).'
date_created: 2019-05-26T21:59:14Z
date_published: 2020-07-01T00:00:00Z
date_updated: 2023-08-28T08:38:48Z
day: '01'
department:
- _id: LaEr
doi: 10.1142/S2010326320500069
ec_funded: 1
external_id:
arxiv:
- '1806.08751'
isi:
- '000547464400001'
intvolume: ' 9'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1806.08751
month: '07'
oa: 1
oa_version: Preprint
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
- _id: 2564DBCA-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '665385'
name: International IST Doctoral Program
publication: 'Random Matrices: Theory and Application'
publication_identifier:
eissn:
- '20103271'
issn:
- '20103263'
publication_status: published
publisher: World Scientific Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Fluctuations for differences of linear eigenvalue statistics for sample covariance
matrices
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 9
year: '2020'
...