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Найдено 5 публикаций
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Статья
Bobkov S., Chistyakov G., Goetze F. Electronic Journal of Probability. 2018. No. 23. P. 1-22.

Under correlation-type conditions, we derive upper bounds of order 1/\sqrt{n} for the Kolmogorov distance between the distributions of weighted sums of dependent summands and the normal law.

Добавлено: 15 октября 2018
Статья
Borodin A., Olshanski G. Electronic Journal of Probability. 2013. Vol. 75. P. 1-43.

The Thoma cone is an infinite-dimensional locally compact space, which is closely related to the space of extremal characters of the infinite symmetric group. In another context, the Thoma cone appears as the set of parameters for totally positive, upper triangular Toeplitz matrices of infinite size.

The purpose of the paper is to construct a family of continuous time Markov processes on the Thoma cone, depending on two continuous parameters. Our construction largely exploits specific properties of the Thoma cone related to its representation-theoretic origin, although we do not use representations directly. On the other hand, we were inspired by analogies with random matrix theory coming from models of Markov dynamics related to orthogonal polynomial ensembles.

We show that our processes possess a number of nice properties, namely: (1) every process X is a Feller process; (2) the infinitesimal generator of X, its spectrum, and the eigenfunctions admit an explicit description; (3) in the equilibrium regime, the finite-dimensional distributions of X can be interpreted as (the laws of) infinite-particle systems with determinantal correlations; (4) the corresponding time-dependent correlation kernel admits an explicit expression, and its structure is similar to that of time-dependent correlation kernels appearing in random matrix theory.

Добавлено: 16 ноября 2013
Статья
Delarue F., Menozzi S., Nualart E. Electronic Journal of Probability. 2015. Vol. 20, Article number 92. No. 92. P. 1-39.

In this paper we prove that the spatially homogeneous Landau equation for Maxwellian molecules can be represented through the product of two elementary stochastic processes. The first one is the Brownian motion on the group of rotations. The second one is, conditionally on the first one, a Gaussian process. Using this representation, we establish sharp multi-scale upper and lower bounds for the transition density of the Landau equation, the multi-scale structure depending on the shape of the support of the initial condition. © 2015, University of Washington. All rights reserved.

Добавлено: 9 октября 2015
Статья
Zhivotovskiy N. Electronic Journal of Probability. 2020. Vol. 25. P. 1-30.
Добавлено: 2 августа 2020
Статья
Konakov V., Menozzi S. Electronic Journal of Probability. 2017. Vol. 22. P. 1-47.
Добавлено: 12 мая 2017