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作者：Bernou, Armand; Fournier, Nicolas
作者单位：Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS)
摘要：We use a probabilistic approach to study the rate of convergence to equilibrium for a collisionless (Knudsen) gas in dimension equal to or larger than 2. The use of a coupling between two stochastic processes allows us to extend and refine, in total variation distance, the polynomial rate of convergence given in (Kinet. Relat. Models 4 (2011) 87-107) and (Comm. Math. Phys. 318 (2013) 375-409). This is, to our knowledge, the first quantitative result in collisionless kinetic theory in dimension...
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作者：Fan, Zhou; Johnstone, Iain M.
作者单位：Yale University; Stanford University
摘要：We study the sample covariance matrix for real-valued data with general population covariance, as well as MANOVA-type covariance estimators in variance components models under null hypotheses of global sphericity. In the limit as matrix dimensions increase proportionally, the asymptotic spectra of such estimators may have multiple disjoint intervals of support, possibly intersecting the negative half line. We show that the distribution of the extremal eigenvalue at each regular edge of the sup...
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作者：Amendola, Carlos; Klueppelberg, Claudia; Lauritzen, Steffen; Tran, Ngoc M.
作者单位：Technical University of Munich; University of Copenhagen; University of Texas System; University of Texas Austin
摘要：Motivated by extreme value theory, max-linear Bayesian networks have been recently introduced and studied as an alternative to linear structural equation models. However, for max-linear systems the classical independence results for Bayesian networks are far from exhausting valid conditional independence statements. We use tropical linear algebra to derive a compact representation of the conditional distribution given a partial observation, and exploit this to obtain a complete description of ...
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作者：Clark, Jeremy Thane
作者单位：University of Mississippi
摘要：We construct and study a family of random continuum polymer mea-sures Mr corresponding to limiting partition function laws recently derived in a weak-coupling regime for polymer models on hierarchical graphs with marginally relevant disorder. The continuum polymers, which we refer to as directed paths, are identified with isometric embeddings of the unit interval [0, 1] into a compact diamond fractal having Hausdorff dimension two, and there is a natural uniform probability measure, mu, over t...
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作者：Hu, Yue; Dong, Jing; Perry, Ohad
作者单位：Columbia University; Northwestern University
摘要：We study an optimal-control problem of polling systems with large switchover times, when a holding cost is incurred on the queues. In particular, we consider a stochastic network with a single server that switches between several buffers (queues) according to a pre-specified order, assuming that the switchover times between the queues are large relative to the processing times of individual jobs. Due to its complexity, computing an optimal control for such a system is prohibitive, and so we in...
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作者：Forman, Noah; Rizzolo, Douglas; Shi, Quan; Winkel, Matthias
作者单位：McMaster University; University of Delaware; University of Mannheim; University of Oxford
摘要：We give a pathwise construction of a two-parameter family of purelyatomic-measure-valued diffusions in which ranked masses of atoms are stationary with the Poisson-Dirichlet(alpha,theta) distributions, for alpha is an element of(0, 1) and theta >= 0. These processes resolve a conjecture of Feng and Sun (Probab. Theory Related Fields 148 (2010) 501-525). We build on our previous work on (alpha, 0)- and (alpha, alpha)-interval partition evolutions. The extension to general theta >= 0 is achieved...
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作者：Bencheikh, Oumaima; Jourdain, Benjamin
作者单位：Inria; Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees
摘要：In this paper, we analyse the rate of convergence of a system of N in-teracting particles with mean-field rank-based interaction in the drift coef-ficient and constant diffusion coefficient. We first adapt arguments by Kolli and Shkolnikov (Ann. Probab. 46 (2018) 1042-1069) to check trajectorial propagation of chaos with optimal rate N-1/2 to the associated stochastic differential equations nonlinear in the sense of McKean. We next relax the assumptions needed by Bossy (Math. Comp. 73 (2004) 7...
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作者：Junge, Matthew; Lyu, Hanbaek
作者单位：City University of New York (CUNY) System; Baruch College (CUNY)
摘要：Ballistic annihilation is an interacting system in which particles placed throughout the real line move at preassigned velocities and annihilate upon colliding. The longstanding conjecture that in the symmetric three-velocity setting there exists a phase transition for the survival of middle-velocity particles was recently resolved by Haslegrave, Sidoravicius, and Tournier. We develop a framework based on a mass transport principle to analyze threevelocity ballistic annihilation with asymmetri...
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作者：Beffara, Vincent; Chhita, Sunil; Johansson, Kurt
作者单位：Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Durham University; Royal Institute of Technology
摘要：Random tilings of the two-periodic Aztec diamond contain three macroscopic regions: frozen, where the tilings are deterministic; rough, where the correlations between dominoes decay polynomially; smooth, where the correlations between dominoes decay exponentially. In a previous paper, the authors found that a certain averaging of height function differences at the rough-smooth interface converged to the extended Airy kernel point process. In this paper, we augment the local geometrical picture...
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作者：Galeati, Lucio; Harang, Fabian A.
作者单位：University of Bonn; University of Oslo
摘要：We investigate the regularizing effect of certain additive continuous perturbations on SDEs with multiplicative fractional Brownian motion (fBm). Traditionally, a Lipschitz requirement on the drift and diffusion coefficients is imposed to ensure existence and uniqueness of the SDE. We show that suitable perturbations restore existence, uniqueness and regularity of the flow for the resulting equation, even when both the drift and the diffusion coefficients are distributional, thus extending the...
