Non-crossing Brownian Paths and Dyson Brownian Motion Under a Moving Boundary
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Statistical Physics"
DOI: 10.1007/s10955-019-02388-z
Abstract: We compute analytically the probability $S(t)$ that a set of $N$ Brownian paths do not cross each other and stay below a moving boundary $g(\tau)= W \sqrt{\tau}$ up to time $t$. We show that for… read more here.
Keywords: tau; dyson brownian; tau sqrt; moving boundary ... See more keywords
Fixed energy universality of Dyson Brownian motion
Sign Up to like & getrecommendations! Published in 2019 at "Advances in Mathematics"
DOI: 10.1016/j.aim.2019.02.010
Abstract: We consider Dyson Brownian motion for classical values of $\beta$ 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 \gtrsim… read more here.
Keywords: brownian motion; energy; energy universality; dyson brownian ... See more keywords
Three phases of multiple SLE driven by non-colliding Dyson’s Brownian motions
Sign Up to like & getrecommendations! Published in 2021 at "Journal of Physics A: Mathematical and Theoretical"
DOI: 10.1088/1751-8121/ac0dee
Abstract: The present paper is concerned with properties of multiple Schramm–Loewner evolutions (SLEs) labelled by a parameter κ ∈ (0, 8]. Specifically, we consider the solution of the multiple Loewner equation driven by a time change… read more here.
Keywords: non colliding; dyson brownian; three phases; phases multiple ... See more keywords
Stochastic weight matrix dynamics during learning and Dyson Brownian motion
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DOI: 10.1103/physreve.111.015303
Abstract: We demonstrate that the update of weight matrices in learning algorithms can be described in the framework of Dyson Brownian motion, thereby inheriting many features of random matrix theory. We relate the level of stochasticity… read more here.
Keywords: dyson brownian; brownian motion; stochastic weight;
The phase transition in the ultrametric ensemble and local stability of Dyson Brownian motion
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DOI: 10.1214/18-ejp197
Abstract: We study the ultrametric random matrix ensemble, whose independent entries have variances decaying exponentially in the metric induced by the tree topology on $\mathbb{N}$, and map out the entire localization regime in terms of eigenfunction… read more here.
Keywords: phase transition; brownian motion; dyson brownian;