Zobrazeno 1 - 10
of 153
pro vyhledávání: '"Horng-Tzer Yau"'
Publikováno v:
Oberwolfach Reports. 19:1501-1550
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::84a4137c87a366171be98da978e0900f
https://doi.org/10.4171/owr/2022/27
https://doi.org/10.4171/owr/2022/27
Publikováno v:
Communications in Mathematical Physics. 396:527-622
We consider Green's functions $G(z):=(H-z)^{-1}$ of Hermitian random band matrices $H$ on the $d$-dimensional lattice $(\mathbb Z/L\mathbb Z)^d$. The entries $h_{xy}=\bar h_{yx}$ of $H$ are independent centered complex Gaussian random variables with
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8543355a4dff84a8ff6464013063a8d5
https://doi.org/10.1007/s00220-022-04474-y
https://doi.org/10.1007/s00220-022-04474-y
Publikováno v:
Journal of the European Mathematical Society. 23:3707-3800
In this paper we establish eigenvector delocalization and bulk universality for L\'{e}vy matrices, which are real, symmetric, $N \times N$ random matrices $\textbf{H}$ whose upper triangular entries are independent, identically distributed $\alpha$-s
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5fa21e3f68539cc2f948e052a960984d
https://doi.org/10.4171/jems/1089
https://doi.org/10.4171/jems/1089
Publikováno v:
Advances in Mathematics. 346:1137-1332
We consider Dyson Brownian motion for classical values of β with deterministic initial data V. We prove that the local eigenvalue statistics coincide with the GOE/GUE in the fixed energy sense after time t ≳ 1 / N if the density of states of V is
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::3728abb590fa14de05f41742df07ce0b
https://doi.org/10.1016/j.aim.2019.02.010
https://doi.org/10.1016/j.aim.2019.02.010
Autor:
Christian Brennecke, Horng-Tzer Yau
Publikováno v:
Journal of Mathematical Physics. 63:073302
We provide a simple extension of Bolthausen's Morita type proof of the replica symmetric formula [E. Bolthausen, Stat. Mech. of Classical and Disordered Systems, pp. 63-93 (2018)] for the Sherrington-Kirkpatrick model and prove the replica symmetry f
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f24768ad3bf4b8235c424b93bb197f0a
https://doi.org/10.1063/5.0073807
https://doi.org/10.1063/5.0073807
Publikováno v:
Ann. Probab. 48, no. 2 (2020), 916-962
We consider the statistics of the extreme eigenvalues of sparse random matrices, a class of random matrices that includes the normalized adjacency matrices of the Erdős–Rényi graph $G(N,p)$. Tracy–Widom fluctuations of the extreme eigenvalues f
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8f6da79db5bbcfe70520e85feb7abf0a
https://doi.org/10.1214/19-aop1378
https://doi.org/10.1214/19-aop1378
Autor:
Jake Marcinek, Horng-Tzer Yau
We study joint eigenvector distributions for large symmetric matrices in the presence of weak noise. Our main result asserts that every submatrix in the orthogonal matrix of eigenvectors converges to a multidimensional Gaussian distribution. The proo
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e4fbb35a32186864ba389a3eee46e79b
Autor:
Craig A. Tracy, Jürg Fröhlich, Jennifer Chayes, George E. Andrews, Harold Widom, Joel L. Lebowitz, Andrew V. Sills, Pavel Bleher, Krishnaswami Alladi, Stephen L Adler, Hugh L. Montgomery, Andrew Odlyzko, Horng-Tzer Yau, Juan M Maldacena
Publikováno v:
Notices of the American Mathematical Society. 68:1
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::ab090ffb756e99898a91ea1d56e3651f
https://doi.org/10.1090/noti2323
https://doi.org/10.1090/noti2323
Autor:
Horng-Tzer Yau, Benjamin Landon
Publikováno v:
Communications in Mathematical Physics. 355:949-1000
We analyze the rate of convergence of the local statistics of Dyson Brownian motion to the GOE/GUE for short times $t=o(1)$ with deterministic initial data V . Our main result states that if the density of states of $V$ is bounded both above and away
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2834ca3b1bf886e254dd6c3e1241e19e
https://doi.org/10.1007/s00220-017-2955-1
https://doi.org/10.1007/s00220-017-2955-1