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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：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：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：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...
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作者：Menz, Georg; Tassy, Martin
作者单位：University of California System; University of California Los Angeles; Dartmouth College
摘要：We show the existence of a variational principle for graph homomorphisms from Z(m) to a d-regular tree. The technique is based on a discrete Kirszbraun theorem and a concentration inequality obtained through the dynamics of the model. As another consequence of the concentration inequality we also obtain the existence of a continuum of translation-invariant ergodic gradient Gibbs measures for graph homomorphisms from Z(m) to a regular tree. The method is sufficiently robust such that it could b...
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作者：Beliaev, Dmitry; McAuley, Michael; Muirhead, Stephen
作者单位：University of Oxford; University of London; King's College London; University of London; Queen Mary University London
摘要：The Nazarov-Sodin constant describes the average number of nodal set components of smooth Gaussian fields on large scales. We generalise this to a functional describing the corresponding number of level set components for arbitrary levels. Using results from Morse theory, we express this functional as an integral over the level densities of different types of critical points, and as a result deduce the absolute continuity of the functional as the level varies. We further give upper and lower b...
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作者：Hazla, Jan; Mossel, Elchanan; Ross, Nathan; Zheng, Guangqu
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Massachusetts Institute of Technology (MIT); University of Melbourne; University of Kansas
摘要：We study the phenomenon of intransitivity in models of dice and voting. First, we follow a recent thread of research for n-sided dice with pairwise ordering induced by the probability, relative to 1/2, that a throw from one die is higher than the other. We build on a recent result of Polymath showing that three dice with i.i.d. faces drawn from the uniform distribution on {1, ... , n} and conditioned on the average of faces equal to (n+1)/2 are intransitive with asymptotic probability 1/4. We ...
