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作者：Major, P
作者单位：HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; Hungarian Academy of Sciences
摘要：Let xi(1), xi(2),... be a sequence of i.i.d. random variables, and consider the elementary symmetric polynomial S-(k)(n) of order k = k(n) of the first n elements xi(1),..., xi(n) of this sequence. We are interested in the limit behavior of S-(k)(n) with an appropriate transformation if k(n)/n --> alpha, 0 < alpha < 1. Since k(n) --> infinity as n --> infinity, the classical methods cannot be applied in this case and new kinds of results appear. We solve the problem under some conditions which...
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作者：Giné, E; Guillou, A
作者单位：University of Connecticut; Sorbonne Universite
摘要：First- and second-order laws of the iterated logarithm are obtained for both the Nelson-Aalen and the Kaplan-Meier estimators in the random censorship model, uniform up to a large order statistic of the censored data. The rates for the first-order processes are exact except for constants. The LIL for the second-order processes (where one subtracts a linear, empirical process, term from the difference between the original process and the estimator), uniform over fixed intervals, is also proved....
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作者：Hargé, G
作者单位：Universite Paris Saclay
摘要：Our purpose is to prove a particular case of a conjecture concerning the Gaussian measure of the intersection of two symmetric convex sets of R-n. This conjecture states that the measure of the intersection is greater or equal to the product of the measures. In this paper, we prove the inequality when one of the two convex sets is a symmetric ellipsoid and the other one is simply symmetric. The general case is still open.
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作者：Lawler, GF; Werner, W
作者单位：Duke University; Universite Paris Saclay
摘要：We derive properties concerning all intersection exponents for planar Brownian motion and we define generalized exponents that, loosely speaking, correspond to noninteger numbers of Brownian paths. Some of these properties lead to general conjectures concerning the exact value of these exponents.
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作者：Khoshnevisan, D; Shi, Z
作者单位：Utah System of Higher Education; University of Utah; Sorbonne Universite
摘要：The main goal of this paper is to present an explicit capacity estimate for hitting probabilities of the Brownian sheet. As applications, we determine the escape rates of the Brownian sheet and also obtain a local intersection equivalence between the Brownian sheet and the additive Brownian motion. Other applications concern quasi-sure properties in Wiener space.
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作者：Pemantle, R; Volkov, S
作者单位：University of Wisconsin System; University of Wisconsin Madison
摘要：A stochastic process called vertex-reinforced random walk (VRRW) is defined in Pemantle [Ann. Probab. 16 1229-1241]. We consider this process in the case where the underlying graph is an infinite chain (i.e., the one-dimensional integer lattice). We show that the range is almost surely finite, that at least five points are visited infinitely often almost surely and that with positive probability the range contains exactly five points. There are always points visited infinitely often but at a s...
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作者：Bobkov, SG
作者单位：Syktyvkar State University
摘要：We study the question on how large the size of singular component of translates of product probability measures can be in terms of Fisher information. We then prove some shift inequalities.
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作者：Steinsaltz, D
作者单位：University of California System; University of California Berkeley
摘要：An iterated function system on X subset of Rd is defined by successively applying an i.i.d. sequence of random Lipschitz functions from X to X. This paper shows how F-n = f(1) circle...circle f(n) may converge even in the absence of the strong contraction conditions, for instance, Lipschitz constant smaller than 1 on average, which earlier work has required. Instead, it is posited that there be a region of contraction which compensates for the noncontractive or even expansive part of the funct...
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作者：Ancona, A; Lyons, R; Peres, Y
作者单位：Universite Paris Saclay; Indiana University System; Indiana University Bloomington; Hebrew University of Jerusalem; University of California System; University of California Berkeley
摘要：Let {X-n} be a transient reversible Markov chain and let f be a function on the state space with finite Dirichlet energy. We prove crossing inequalities for the process (f(X-n)}(n greater than or equal to 1) and show that it converges almost surely and in L-2. Analogous results are also established for reversible diffusions on Riemannian manifolds.
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作者：Wang, FY
作者单位：Beijing Normal University; University of Bielefeld
摘要：By using the maximum principle and analysis of heat semigroups, Harnack inequalities are studied for log-Sobolev functions. From this, some lower bound estimates of the log-Sobolev constant are presented by using the spectral gap inequality and the coupling method. The resulting inequalities either recover or improve the corresponding ones proved by Chung and Yau. Especially, Harnack inequalities and estimates of log-Sobolev constants can be dimension-free.
