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作者：Sellke, Mark
作者单位：Stanford University
摘要：In the Gilbert-Shannon-Reeds shuffle, a deck of N cards is cut into two approximately equal parts which are riffled together uniformly at random. Bayer and Diaconis (Ann. Appl. Probab. 2 294-313) famously showed that this Markov chain undergoes cutoff in total variation after 3 log(N) 2log(2) shuffles. We establish cutoff for the more general asymmetric riffle shuffles in which one cuts the deck into differently sized parts. The value of the cutoff point confirms a conjecture of Lalley from 20...
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作者：Legrand, Alexandre; Petrelis, Nicolas
作者单位：Nantes Universite
摘要：The present paper is dedicated to the 2-dimensional Interacting Partially Directed Self Avoiding Walk constrained to remain in the upper-half plane and interacting with the horizontal axis. This model has originally been introduced to investigate the behavior of a homopolymer dipped in a poor solvent and adsorbed along a horizontal hard wall. It is known to undergo a collapse transition between an extended phase, inside which typical configurations of the polymer have a large horizontal extens...
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作者：Izyurov, Konstantin
作者单位：University of Helsinki
摘要：We prove the convergence of multiple interfaces in the critical planar q = 2 random cluster model and provide an explicit description of the scaling limit. Remarkably, the expression for the partition function of the resulting multiple SLE16/3 coincides with the bulk spin correlation in the critical Ising model in the half-plane, after formally replacing a position of each spin and its complex conjugate with a pair of points on the real line. As a corollary we recover Belavin-Polyakov-Zamolodc...
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作者：Magazinov, Alexander; Peled, Ron
作者单位：Tel Aviv University
摘要：We derive two concentration inequalities for linear functions of log-concave distributions: an enhanced version of the classical Brascamp-Lieb concentration inequality and an inequality quantifying log-concavity of marginals in a manner suitable for obtaining variance and tail probability bounds. These inequalities are applied to the statistical mechanics problem of estimating the fluctuations of random surfaces of the del phi type. The classical Brascamp-Lieb inequality bounds the fluctuation...
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作者：Pete, Gabor; Timar, Adam
作者单位：HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; University of Iceland
摘要：We prove the rather counterintuitive result that there exist finite transitive graphs H and integers k such that the Free Uniform Spanning Forest in the direct product of the k-regular tree and H has infinitely many trees almost surely. This shows that the number of trees in the FUSF is not a quasi-isometry invariant. Moreover, we give two different Cayley graphs of the same virtu-ally free group such that the FUSF has infinitely many trees in one, but is connected in the other, answering a qu...
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作者：Pitman, Jim; Tang, Wenpin
作者单位：University of California System; University of California Berkeley; Columbia University
摘要：This paper is concerned with the limit laws of the extreme order statistics derived from a symmetric Laplace walk. We provide two different descriptions of the point process of the limiting extreme order statistics: a branching representation and a squared Bessel representation. These complementary descriptions expose various hidden symmetries in branching processes and Brownian motion which lie behind some striking formulas found by Schehr and Majumdar (Phys. Rev. Lett. 108 (2012) 040601). In...
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作者：Aru, Juhan; Lupu, Titus; Sepulveda, Avelio
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Universite Paris Cite; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite; Universidad de Chile
摘要：Consider CLE4 in the unit disk, and let l be the loop of the CLE4 surrounding the origin. Schramm, Sheffield and Wilson determined the law of the conformal radius seen from the origin of the domain surrounded by l. We complement their result by determining the law of the extremal distance between and the boundary of the unit disk. More surprisingly, we also compute the joint law of these conformal radius and extremal distance. This law involves first and last hitting times of a one-dimensional...
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作者：Forghani, Behrang; Tiozzo, Giulio
作者单位：College of Charleston; University of Toronto
摘要：We establish the ray and strip approximation criteria for the identification of the Poisson boundary of random walks on locally compact groups. This settles a conjecture from the 1990s by Kaimanovich, who formulated and proved the criterion for discrete groups. The key result is the proof of a version of the Shannon-McMillan-Breiman theorem for locally compact groups. We provide several applications to locally compact groups of isometrics of nonpositively curved spaces, as well as Diestel-Lead...
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作者：Shen, Hao; Smith, Scott A.; Zhu, Rongchan; Zhu, Xiangchan
作者单位：University of Wisconsin System; University of Wisconsin Madison; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Beijing Institute of Technology
摘要：This article studies large N limits of a coupled system of N interacting Phi(4) equations posed over T-d for d = 2, known as the O(N) linear sigma model. Uniform in N bounds on the dynamics are established, allowing us to show convergence to a mean-field singular SPDE, also proved to be globally well posed. Moreover, we show tightness of the invariant measures in the large N limit. For large enough mass, they converge to the (massive) Gaussian free field, the unique invariant measure of the me...
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作者：Paouris, Grigoris; Tikhomirov, Konstantin; Valettas, Petros
作者单位：Texas A&M University System; Texas A&M University College Station; University System of Georgia; Georgia Institute of Technology; University of Missouri System; University of Missouri Columbia; University of Missouri System; University of Missouri Columbia
摘要：We consider the problem of estimating small ball probabilities P[f (G) <= delta E f (G)} for subadditive, positively homogeneous functions f with respect to the Gaussian measure. We establish estimates that depend on global parameters of the underlying function, which take into account analytic and statistical measures, such as the variance and the L-1-norms of its partial derivatives. This leads to dimension-dependent bounds for small ball and lower small deviation estimates for seminorms whe...
