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作者：Goldie, CM; Maller, RA
作者单位：University of Sussex; University of Western Australia
摘要：For a series of randomly discounted terms we give an integral criterion to distinguish between almost-sure absolute convergence and divergence in probability to infinity, these being the only possible forms of asymptotic behavior. This solves the existence problem for a one-dimensional perpetuity that remains from a 1979 study by Vervaat, and yields a complete characterization of the existence of distributional fixed points of a random affine map in dimension one.
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作者：Kaufman, R; Wu, JM
作者单位：University of Illinois System; University of Illinois Urbana-Champaign
摘要：We study bounded p-harmonic functions u defined on a directed tree T with branching order kappa (1 < p < infinity and kappa = 2, 3,...). Denote by BV(u) the set of paths on which u has finite variation and F(u) the set of paths on which rr has a finite limit. Then the infimum of dim BV(u) and the infimum of dim F(u) are equal over all bounded p-harmonic functions on T (with p and kappa fixed); the infimum d(kappa, p) is attained and is strictly between 0 and 1 expect when p = 2 or kappa = 2.
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作者：Jeon, I; March, P; Pittel, B
作者单位：University System of Ohio; Ohio State University
摘要：We study the finite zero-range process with occupancy-dependent rate function g(.). Under the invariant measure, which can be written explicitly in terms of g, particles are distributed over sites and we regard all particles at a fixed site as a cluster. In the density one case, that; is, equal numbers of particles and sites, we determine asymptotically the size of the largest cluster, as the number of particles tends to infinity, and determine? its dependence on the rate function.
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作者：Häggström, O; Schonmann, RH; Steif, JE
作者单位：Chalmers University of Technology; University of California System; University of California Los Angeles
摘要：Say that a graph has persistent transition if the Ising model on the graph can exhibit a phase transition (nonuniqueness of Gibbs measures) in the presence of a nonzero external field. we show that for nonamenable graphs, for Bernoulli percolation with p close to 1, all the infinite clusters have persistent transition. On the other hand, we show that for transitive amenable graphs, the infinite clusters fbr any stationary percolation do not have persistent transition This extends a result of G...
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作者：O'Cinneide, C
作者单位：Purdue University System; Purdue University
摘要：We present a method for proving Perron-Frobenius eigenvalue inequalities. The method is to apply Jensen's inequality to the change in a random evolution over a regenerative cycle of the underlying finite-state Markov chain. One of the primary benefits of the method is that it readily gives necessary and sufficient conditions for strict inequality. It also gives insights into some of the conjectures of J. E. Cohen. Ney and Nummelin's Hypothesis 2 arises here as a condition for strict inequality...
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作者：Donnelly, P; Evans, SN; Fleischmann, K; Kurtz, TG; Zhou, XW
作者单位：University of Oxford; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; University of California System; University of California Berkeley; University of Wisconsin System; University of Wisconsin Madison; University of Wisconsin System; University of Wisconsin Madison; University of British Columbia
摘要：Analogues of stepping-stone models are considered where the site-space is continuous, the migration process is a general Markov process, and the type-space is infinite. Such processes were defined in previous work of the second author by specifying a Feller transition semigroup in terms of expectations of suitable functionals for systems of coalescing Markov processes. An alternative representation is obtained here in terms of a limit of interacting particle systems. It is shown that, under a ...
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作者：Cerf, R; Pisztora, A
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay; Carnegie Mellon University
摘要：We study the phase separation phenomenon ilo the Ising model in dimensions d greater than or equal to 3. To this end we work in a large box with plus boundary conditions and we condition the system to have an excess amount of negative spins so that the empirical magnetization is smaller than the spontaneous magnetization m*. We confirm the prediction of the phenomenological theory by proving that with high probability a single droplet of the minus phase emerges surrounded by the plus phase. Mo...
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作者：Deheuvels, P; Einmahl, JH
作者单位：Sorbonne Universite; Eindhoven University of Technology
摘要：We prove functional limit laws for the increment functions of empirical processes based upon randomly right-censored data. The increment sizes we consider are classified into different classes covering the whole possible spectrum. We apply these results to obtain a description of the strong limiting behavior of a series of estimators of local functionals of lifetime distributions. In particular, we treat the case of kernel density and hazard rate estimators.
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作者：Gantert, N
作者单位：Technical University of Berlin
摘要：We consider an infinite Galton-Watson tree Gamma and label the vertices nu with a collection of i.i.d. random variables (Y-nu)(nu is an element of Gamma). In the case where the upper tail of the distribution of Y-nu is semiexponential, we then determine the speed of the corresponding tree-indexed random walk. In contrast to the classical case where the random variables Y-nu have finite exponential moments, the normalization in the definition of the speed depends on the distribution of Y-nu. In...
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作者：Kuelbs, J
作者单位：University of Wisconsin System; University of Wisconsin Madison
摘要：The existence of a dominating point for an open convex set and a corresponding representation formula for large deviation probabilities are established in the infinite-dimensional setting under conditions which are both necessary and sufficient and follow from those used previously in R-d. A precise nonlogarithmic estimate of large deviation probabilities applicable to Gaussian measures is also included.
