Zobrazeno 1 - 10
of 409
pro vyhledávání: '"Bourgade, P."'
We prove that under the Brownian evolution on large non-Hermitian matrices the log-determinant converges in distribution to a 2+1 dimensional Gaussian field in the Edwards-Wilkinson regularity class, namely it is logarithmically correlated for the pa
Externí odkaz:
http://arxiv.org/abs/2409.02902
We determine to leading order the maximum of the characteristic polynomial for Wigner matrices and $\beta$-ensembles. In the special case of Gaussian-divisible Wigner matrices, our method provides universality of the maximum up to tightness. These ar
Externí odkaz:
http://arxiv.org/abs/2312.13335
We prove a lower bound on the maximum of the Riemann zeta function in a typical short interval on the critical line. Together with the upper bound from the previous work of the authors, this implies tightness of $$ \max_{|h|\leq 1}|\zeta(\tfrac 12+{\
Externí odkaz:
http://arxiv.org/abs/2307.00982
Autor:
Barbara Bourgade, M. Ahsanul Islam
Publikováno v:
Frontiers in Microbiology, Vol 15 (2024)
Thermophilic acetogens are gaining recognition as potent microbial cell factories, leveraging their unique metabolic capabilities to drive the development of sustainable biotechnological processes. These microorganisms, thriving at elevated temperatu
Externí odkaz:
https://doaj.org/article/401b2ec701f442b281d8f3e787e60804
Autor:
Bourgade, Paul, Falconet, Hugo
We establish the first connection between $2d$ Liouville quantum gravity and natural dynamics of random matrices. In particular, we show that if $(U_t)$ is a Brownian motion on the unitary group at equilibrium, then the measures $$ |\det(U_t - e^{i \
Externí odkaz:
http://arxiv.org/abs/2206.03029
This paper characterizes the annealed, topological complexity (both of total critical points and of local minima) of the elastic manifold. This classical model of a disordered elastic system captures point configurations with self-interactions in a r
Externí odkaz:
http://arxiv.org/abs/2105.05051
Publikováno v:
Prob. Math. Phys. 3 (2022) 731-789
We give simple criteria to identify the exponential order of magnitude of the absolute value of the determinant for wide classes of random matrix models, not requiring the assumption of invariance. These include Gaussian matrices with covariance prof
Externí odkaz:
http://arxiv.org/abs/2105.05000
In the setting of generic $\beta$-ensembles, we use the loop equation hierarchy to prove a local law with optimal error up to a constant, valid on any scale including microscopic. This local law has the following consequences. (i) The optimal rigidit
Externí odkaz:
http://arxiv.org/abs/2103.06841
Autor:
Cueff, Sebastien, Taute, Arnaud, Bourgade, Antoine, Lumeau, Julien, Monfray, Stephane, Song, Qinghua, Genevet, Patrice, Letartre, Xavier, Berguiga, Lotfi
We experimentally demonstrate a very large dynamic optical reflection modulation from a simple unpatterned layered stack of phase-change materials ultrathin films. Specifically, we theoretically and experimentally demonstrate that properly designed d
Externí odkaz:
http://arxiv.org/abs/2009.02532
By analogy with conjectures for random matrices, Fyodorov-Hiary-Keating and Fyodorov-Keating proposed precise asymptotics for the maximum of the Riemann zeta function in a typical short interval on the critical line. In this paper, we settle the uppe
Externí odkaz:
http://arxiv.org/abs/2007.00988