Zobrazeno 1 - 10
of 21
pro vyhledávání: '"Kevin Schnelli"'
Publikováno v:
Forum of Mathematics, Sigma, Vol 9 (2021)
We prove that the energy of any eigenvector of a sum of several independent large Wigner matrices is equally distributed among these matrices with very high precision. This shows a particularly strong microcanonical form of the equipartition principl
Externí odkaz:
https://doaj.org/article/33e784f67bd34e6eb8fc9d43e091b598
Autor:
Kevin Schnelli, Yuanyuan Xu
Publikováno v:
The Annals of Applied Probability. 33
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::b403483cb864f5bd09bf054cb7fe9d80
https://doi.org/10.1214/22-aap1826
https://doi.org/10.1214/22-aap1826
Publikováno v:
Journal d'Analyse Mathématique. 142:323-348
We consider the free additive convolution of two probability measures $\mu$ and $\nu$ on the real line and show that $\mu\boxplus\nu$ is supported on a single interval if $\mu$ and $\nu$ each has single interval support. Moreover, the density of $\mu
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1b4501e4c6239c63d8ff1963a40f47ca
https://doi.org/10.1007/s11854-020-0135-2
https://doi.org/10.1007/s11854-020-0135-2
Autor:
Kevin Schnelli, Yuanyuan Xu
Publikováno v:
Communications in mathematical physics. 393(2)
We show that the fluctuations of the largest eigenvalue of a real symmetric or complex Hermitian Wigner matrix of size $N$ converge to the Tracy--Widom laws at a rate $O(N^{-1/3+\omega})$, as $N$ tends to infinity. For Wigner matrices this improves t
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::13db0df31a859a7e35cbf094f0ed8a34
https://pubmed.ncbi.nlm.nih.gov/35765414
https://pubmed.ncbi.nlm.nih.gov/35765414
We prove that the energy of any eigenvector of a sum of several independent large Wigner matrices is equally distributed among these matrices with very high precision. This shows a particularly strong microcanonical form of the equipartition principl
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4f1946a3645464be96db84f6679675c3
Autor:
Kevin Schnelli, Ji Oon Lee
Publikováno v:
Probability Theory and Related Fields. 171:543-616
We consider spectral properties and the edge universality of sparse random matrices, the class of random matrices that includes the adjacency matrices of the Erdős–Renyi graph model G(N, p). We prove a local law for the eigenvalue density up to th
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::2519201a3f11e547d7ed1e00242db35a
https://doi.org/10.1007/s00440-017-0787-8
https://doi.org/10.1007/s00440-017-0787-8
Publikováno v:
Ann. Appl. Probab. 29, no. 5 (2019), 3006-3036
We consider spectral properties of sparse sample covariance matrices, which includes biadjacency matrices of the bipartite Erdős–Renyi graph model. We prove a local law for the eigenvalue density up to the upper spectral edge. Under a suitable con
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::88e83f5bd5b62c1a1606f2ea6659d057
https://projecteuclid.org/euclid.aoap/1571385628
https://projecteuclid.org/euclid.aoap/1571385628
We consider $N$ by $N$ deformed Wigner random matrices of the form $X_N=H_N+A_N$, where $H_N$ is a real symmetric or complex Hermitian Wigner matrix and $A_N$ is a deterministic real bounded diagonal matrix. We prove a universal Central Limit Theorem
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::30b048ed993d148dc1b164dbe531891e
http://arxiv.org/abs/1909.12821
http://arxiv.org/abs/1909.12821
Publikováno v:
Ann. Probab. 47, no. 3 (2019), 1270-1334
Let $U$ and $V$ be two independent $N$ by $N$ random matrices that are distributed according to Haar measure on $U(N)$. Let $\Sigma$ be a non-negative deterministic $N$ by $N$ matrix. The single ring theorem [26] asserts that the empirical eigenvalue
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::bf4fa9302bc03a8b01c3bab8230795c4
https://doi.org/10.1214/18-aop1284
https://doi.org/10.1214/18-aop1284
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 asymptoticall
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e8eff64097159bc29b33e01206d94f06