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
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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
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;