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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：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：Bloom, Thomas; Dauvergne, Duncan
作者单位：University of Toronto
摘要：We consider random polynomials of the form H-n(z) = Sigma(n)(j=0)xi(j)q(j)(z) where the {xi(j)} are i.i.d. nondegenerate complex random variables, and the {q(j)(z)} are orthonormal polynomials with respect to a compactly supported measure tau satisfying the Bernstein-Markov property on a regular compact set K subset of C. We show that if P(|xi(0)| > e(vertical bar z vertical bar)) = o(vertical bar z vertical bar(-1)), then the normalized counting measure of the zeros of H-n converges weakly in...
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作者：Jiao, Yong; Osekowski, Adam; Wu, Lian
作者单位：Central South University; University of Warsaw
摘要：We introduce a notion of strong differential subordination of noncommutative semimartingales, extending Burkholder's definition from the classical case (Ann. Probab. 22 (1994) 995-1025). Then we establish the maximal weak-type (1, 1) inequality under the additional assumption that the dominating process is a submartingale. The proof rests on a significant extension of the maximal weak-type estimate of Cuculescu and a Gundy-type decomposition of an arbitrary noncommutative submartingale. We als...
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作者：Grothaus, Martin; Wang, Feng-Yu
作者单位：University of Kaiserslautern; Tianjin University
摘要：For a contraction C-0-semigroup on a separable Hilbert space, the decay rate is estimated by using the weak Poincare inequalities for the symmetric and antisymmetric part of the generator. As applications, nonexponential convergence rate is characterized for a class of degenerate diffusion processes, so that the study of hypocoercivity is extended. Concrete examples are presented.
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作者：Chen, Xian; Ma, Zhi-Ming; Peng, Xue
作者单位：Xiamen University; Sichuan University
摘要：For a given quasi-regular positivity preserving coercive form, we construct a family of (sigma-finite) distribution flows associated with the semigroup of the form. The canonical cadlag process equipped with the distribution flows behaves like a strong Markov process. Moreover, employing distribution flows we can construct optional measures and establish Revuz correspondence between additive functionals and smooth measures. The results obtained in this paper will enable us to perform a kind of...
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作者：Guerra Aguilar, Enrique
作者单位：Pontificia Universidad Catolica de Chile
摘要：We prove a ballistic strong law of large numbers and an invariance principle for random walks in strong mixing environments, under condition (T) of Sznitman (cf. Ann. Probab. 29 (2001) 724-765). This weakens for the first time Kalikow's ballisticity assumption on mixing environments and proves the existence of arbitrary finite order moments for the approximate regeneration time of F. Comets and O. Zeitouni (Israel J. Math. 148 (2005) 87-113). The main technical tool in the proof is the introdu...
