Zobrazeno 1 - 10
of 30
pro vyhledávání: '"Poplavskyi, Mihail"'
Publikováno v:
Entropy 2023, 25(1), 74
Complex eigenvalues of random matrices $J=\text{GUE }+ i\gamma \diag (1, 0, \ldots, 0)$ provide the simplest model for studying resonances in wave scattering from a quantum chaotic system via a single open channel. It is known that in the limit of la
Externí odkaz:
http://arxiv.org/abs/2211.00180
Autor:
Gebert, Martin, Poplavskyi, Mihail
Let $O(2n+\ell)$ be the group of orthogonal matrices of size $\left(2n+\ell\right)\times \left(2n+\ell\right)$ equipped with the probability distribution given by normalized Haar measure. We study the probability \begin{equation*} p_{2n}^{\left(\ell\
Externí odkaz:
http://arxiv.org/abs/1905.03154
Autor:
Poplavskyi, Mihail, Schehr, Gregory
Publikováno v:
Phys. Rev. Lett. 121, 150601 (2018)
We compute the persistence for the $2d$-diffusion equation with random initial condition, i.e., the probability $p_0(t)$ that the diffusion field, at a given point ${\bf x}$ in the plane, has not changed sign up to time $t$. For large $t$, we show th
Externí odkaz:
http://arxiv.org/abs/1806.11275
Publikováno v:
Annales Henri Poincare 2018 Dec 1 (Vol. 19, No. 12, pp. 3635-3662). Springer International Publishing
A class of interacting particle systems on $\mathbb{Z}$, involving instantaneously annihilating or coalescing nearest neighbour random walks, are shown to be Pfaffan point processes for all deterministic initial conditions. As diffusion limits, expli
Externí odkaz:
http://arxiv.org/abs/1507.01843
Publikováno v:
The Annals of Applied Probability 2016, Vol. 26, No. 5, 2733-2753
We study the large-$n$ limit of the probability $p_{2n,2k}$ that a random $2n\times 2n$ matrix sampled from the real Ginibre ensemble has $2k$ real eigenvalues. We prove that, $$\lim_{n\rightarrow \infty}\frac {1}{\sqrt{2n}} \log p_{2n,2k}=\lim_{n\ri
Externí odkaz:
http://arxiv.org/abs/1503.07926
Autor:
Poplavskyi, Mihail
Publikováno v:
Journal of Mathematical Physics, Analysis, Geometry: 2012, v.8, No. 4, p. 367-392
Using the results on the $1/n$-expansion of the Verblunsky coefficients for a class of polynomials orthogonal on the unit circle with $n$ varying weight, we prove that the local eigenvalue statistic for unitary matrix models is independent of the for
Externí odkaz:
http://arxiv.org/abs/1306.6892
Autor:
Poplavskyi, Mihail
Publikováno v:
J. Math. Phys. 53, 043510 (2012)
We present an asymptotic analysis of the Verblunsky coefficients for the polynomials orthogonal on the unit circle with the varying weight $e^{-nV(\cos x)}$, assuming that the potential $V$ has four bounded derivatives on $[-1,1]$ and the equilibrium
Externí odkaz:
http://arxiv.org/abs/1006.5515
Autor:
Poplavskyi, Mihail
Publikováno v:
Journal of Mathematical Physics, Analysis, Geometry: 2009, v. 5, No 3, p. 245-274
We give a proof of universality in the bulk of spectrum of unitary matrix models, assuming that the potential is globally $C^{2}$ and locally $C^{3}$ function. The proof is based on the determinant formulas for correlation functions in terms of polyn
Externí odkaz:
http://arxiv.org/abs/0804.3165
Publikováno v:
The Annals of Applied Probability, 2017 Jun 01. 27(3), 1395-1413.
Externí odkaz:
https://www.jstor.org/stable/26361405
Publikováno v:
The Annals of Applied Probability, 2016 Oct 01. 26(5), 2733-2753.
Externí odkaz:
http://www.jstor.org/stable/24810112