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作者：Campese, Simon; Nourdin, Ivan; Nualart, David
作者单位：University of Luxembourg; University of Kansas
摘要：Let Y = (Y(t))(t >= 0) be a zero-mean Gaussian stationary process with covariance function rho : R -> R satisfying rho (0) = 1. Let f : R -> R be a square-integrable function with respect to the standard Gaussian measure, and suppose the Hermite rank of f is d >= 1. If integral(R) vertical bar rho(s)vertical bar(d) ds < infinity, then the celebrated Breuer-Major theorem (in its continuous version) asserts that the finite-dimensional distributions of Z(epsilon) := root epsilon integral(./epsilo...
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作者：Borgs, Christian; Chayes, Jennifer T.; Cohn, Henry; Veitch, Victor
作者单位：Microsoft; Columbia University
摘要：Recent work has introduced sparse exchangeable graphs and the associated graphex framework, as a generalization of dense exchangeable graphs and the associated graphon framework. The development of this subject involves the interplay between the statistical modeling of network data, the theory of large graph limits, exchangeability and network sampling. The purpose of the present paper is to clarify the relationships between these subjects by explaining each in terms of a certain natural sampl...
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作者：Gorin, Vadim; Petrov, Leonid
作者单位：Massachusetts Institute of Technology (MIT); Kharkevich Institute for Information Transmission Problems of the RAS; University of Virginia
摘要：We consider the N-particle noncolliding Bernoulli random walk-a discrete time Markov process in Z(N) obtained from a collection of N independent simple random walks with steps is an element of {0, 1} by conditioning that they never collide. We study the asymptotic behavior of local statistics of this process started from an arbitrary initial configuration on short times T << N as N -> +infinity. We show that if the particle density of the initial configuration is bounded away from 0 and 1 down...
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作者：Maillard, Pascal; Pain, Michel
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay; Universite PSL; Ecole Normale Superieure (ENS); Centre National de la Recherche Scientifique (CNRS)
摘要：Let (Z(t))(t >= 0) denote the derivative martingale of branching Brownian motion, that is, the derivative with respect to the inverse temperature of the normalized partition function at critical temperature. A well-known result by Lalley and Sellke (Ann. Probab. 15 (1987) 1052-1061) says that this martingale converges almost surely to a limit Z(infinity), positive on the event of survival. In this paper our concern is the fluctuations of the derivative martingale around its limit. A corollary ...
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作者：Okada, Izumi
作者单位：Tokyo University of Science
摘要：As Dembo (In Lectures on Probability Theory and Statistics (2005) 1-101 Springer, and International Congress of Mathematicians, Vol. III (2006) 535-558, Eur. Math. Soc.) suggested, we consider the problem of late points for a simple random walk in two dimensions. It has been shown that the exponents for the number of pairs of late points coincide with those of favorite points and high points in the Gaussian free field, whose exact values are known. We determine the exponents for the number of ...
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作者：Benoist, Stephane; Hongler, Clement
作者单位：Columbia University; Massachusetts Institute of Technology (MIT); Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
摘要：In this paper, we consider the set of interfaces between + and - spins arising for the critical planar Ising model on a domain with + boundary conditions, and show that it converges to nested CLE3. Our proof relies on the study of the coupling between the Ising model and its random cluster (FK) representation, and of the interactions between FK and Ising interfaces. The main idea is to construct an exploration process starting from the boundary of the domain, to discover the Ising loops and to...
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作者：Watanabe, Toshiro
作者单位：University of Aizu
摘要：We show that the class of convolution equivalent distributions and the class of locally subexponential distributions are not closed under convolution roots. It gives a negative answer to the classical conjectures of Embrechts and Goldie. Moreover, we establish two sufficient conditions in order that the class of convolution equivalent distributions is closed under convolution roots.
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作者：Merle, Mathieu; Salez, Justin
作者单位：Universite Paris Cite
摘要：We study the mixing time of the unit-rate zero-range process on the complete graph, in the regime where the number n of sites tends to infinity while the density of particles per site stabilizes to some limit rho > 0. We prove that the worst-case total-variation distance to equilibrium drops abruptly from 1 to 0 at time n(rho + 1/2 rho(2)). More generally, we determine the mixing time from an arbitrary initial configuration. The answer turns out to depend on the largest initial heights in a re...
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作者：Backhausz, Agnes; Szegedy, Balazs
作者单位：HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; Eotvos Lorand University
摘要：Let d >= 3 be fixed and G be a large random d-regular graph on n vertices. We show that if n is large enough then the entry distribution of every almost eigenvector of G(with entry sum 0 and normalized to have length root n) is close to some Gaussian distribution N(0, sigma) in the weak topology where 0 <= sigma <= 1. Our theorem holds even in the stronger sense when many entries are looked at simultaneously in small random neighborhoods of the graph. Furthermore, we also get the Gaussianity o...
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作者：Sasai, Takeyuki; Miyabe, Kenshi; Takemura, Akimichi
作者单位：University of Tokyo; Meiji University; Shiga University
摘要：We prove an Erdos-Feller-Kolmogorov-Petrowsky law of the iterated logarithm for self-normalized martingales. Our proof is given in the framework of the game-theoretic probability of Shafer and Vovk. Like many other game-theoretic proofs, our proof is self-contained and explicit.
