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作者：Chatterjee, Sourav; Diaconis, Persi
作者单位：Stanford University; Stanford University
摘要：We show that the convergence of finite state space Markov chains to stationarity can often be considerably speeded up by alternating every step of the chain with a deterministic move. Under fairly general conditions, we show that not only do such schemes exist, they are numerous.
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作者：Gubinelli, Massimiliano; Perkowski, Nicolas
作者单位：University of Bonn; University of Bonn; Free University of Berlin
摘要：We develop a martingale approach for a class of singular stochastic PDEs of Burgers type (including fractional and multi-component Burgers equations) by constructing a domain for their infinitesimal generators. It was known that the domainmust have trivial intersection with the usual cylinder test functions, and to overcome this difficulty we import some ideas from paracontrolled distributions to an infinite dimensional setting in order to construct a domain of controlled functions. Using the ...
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作者：Wong, Mo Dick
作者单位：University of Oxford
摘要：In this article we study the tail probability of the mass of Gaussian multiplicative chaos. With the novel use of a Tauberian argument and Goldie's implicit renewal theorem, we provide a unified approach to general log-correlated Gaussian fields in arbitrary dimension and derive precise first order asymptotics of the tail probability, resolving a conjecture of Rhodes and Vargas. The leading order is described by a universal constant that captures the generic property of Gaussian multiplicative...
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作者：Ahidar-Coutrix, A.; Le Gouic, T.; Paris, Q.
作者单位：Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS); HSE University (National Research University Higher School of Economics)
摘要：This paper provides rates of convergence for empirical (generalised) barycenters on compact geodesic metric spaces under general conditions using empirical processes techniques. Our main assumption is termed a variance inequality and provides a strong connection between usual assumptions in the field of empirical processes and central concepts of metric geometry. We study the validity of variance inequalities in spaces of non-positive and non-negative Aleksandrov curvature. In this last scenar...
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作者：Belius, David; Rosen, Jay; Zeitouni, Ofer
作者单位：University of Basel; City University of New York (CUNY) System; College of Staten Island (CUNY); Weizmann Institute of Science; New York University
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作者：Jarai, Antal A.; Ruszel, Wioletta M.; Saada, Ellen
作者单位：University of Bath; Delft University of Technology; Utrecht University; Universite Paris Cite; IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom SudParis; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We show that in Abelian sandpiles on infinite Galton-Watson trees, the probability that the total avalanche has more than t topplings decays as t(-1/2). We prove both quenched and annealed bounds, under suitable moment conditions. Our proofs are based on an analysis of the conductance martingale of Morris (Probab Theory Relat Fields 125:259-265, 2003), thatwas previously used by Lyons et al. (Electron J Probab 13(58):1702-1725, 2008) to study uniform spanning forests on Z(d), d >= 3, and other...
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作者：Brennan, Matthew; Bresler, Guy; Nagaraj, Dheeraj
作者单位：Massachusetts Institute of Technology (MIT)
摘要：Random graphs with latent geometric structure are popular models of social and biological networks, with applications ranging from network user profiling to circuit design. These graphs are also of purely theoretical interest within computer science, probability and statistics. A fundamental initial question regarding these models is: when are these random graphs affected by their latent geometry and when are they indistinguishable from simpler models without latent structure, such as the Erdo...
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作者：Roeckner, Michael; Xie, Longjie; Zhang, Xicheng
作者单位：University of Bielefeld; Jiangsu Normal University; Wuhan University
摘要：We prove the superposition principle for probability measure-valued solutions to non-local Fokker-Planck-Kolmogorov equations, which in turn yields the equivalence between martingale problems for stochastic differential equations with jumps and such non-local partial differential equations with rough coefficients. As an application, we obtain a probabilistic representation for weak solutions of fractional porous media equations.
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作者：FitzGerald, Will; Warren, Jon
作者单位：University of Sussex; University of Warwick
摘要：This paper proves an equality in law between the invariant measure of a reflected system of Brownian motions and a vector of point-to-line last passage percolation times in a discrete random environment. A consequence describes the distribution of the all-time supremum of Dyson Brownian motion with drift. A finite temperature version relates the point-to-line partition functions of two directed polymers, with an inverse-gamma and a Brownian environment, and generalises Dufresne's identity. Our...
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作者：Ganguly, Shirshendu; Sarkar, Sourav
作者单位：University of California System; University of California Berkeley; University of Toronto
摘要：Stochastic point processes with Coulomb interactions arise in various natural examples of statistical mechanics, random matrices and optimization problems. Often such systems due to their natural repulsion exhibit remarkable hyperuniformity properties, that is, the number of points landing in any given region fluctuates at a much smaller scale compared to that of a set of i.i.d. random points. A well known conjecture from physics appearing in the works of Jancovici, Lebowitz, Manificat, Martin...
