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作者：Seppalainen, Timo
作者单位：University of Wisconsin System; University of Wisconsin Madison
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作者：Pillai, Natesh S.; Smith, Aaron
作者单位：Harvard University; University of Ottawa
摘要：We study a kinetically constrained Ising process (KCIP) associated with a graph G and density parameter p; this process is an interacting particle system with state space {0, 1}(G), the location of the particles. The number of particles at stationarity follows the Binomial(vertical bar G vertical bar, p) distribution, conditioned on having at least one particle. The constraint in the name of the process refers to the rule that a vertex cannot change its state unless it has at least one neighbo...
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作者：Chen, Le; Cranston, Michael; Khoshnevisan, Davar; Kim, Kunwoo
作者单位：Utah System of Higher Education; University of Utah; University of California System; University of California Irvine
摘要：Given a field {B(x)}x is an element of Z(d) of independent standard Brownian motions, indexed by Z(d), the generator of a suitable Markov process on Z(d), G, and sufficiently nice function sigma : [0, infinity) (bar right arrow) [0, infinity), we consider the influence of the parameter lambda on the behavior of the system, du(t) (x) = (Gu(t))(x) dt + lambda sigma(u(t)(x)) dB(t)(x) [t > 0, x is an element of Z(d)], u(0)(x) = c(0)delta(0)(x). We show that for any lambda > 0 in dimensions one and...
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作者：Lubetzky, Eyal; Sly, Allan
作者单位：New York University; University of California System; University of California Berkeley
摘要：On any locally-finite geometry, the stochastic Ising model is known to be contractive when the inverse-temperature beta is small enough, via classical results of Dobrushin and of Holley in the 1970s. By a general principle proposed by Peres, the dynamics is then expected to exhibit cutoff. However, so far cutoff for the Ising model has been confirmed mainly for lattices, heavily relying on amenability and log Sobolev inequalities. Without these, cutoff was unknown at any fixed beta > 0, no mat...
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作者：Sabot, Christophe; Tarres, Pierre; Zeng, Xiaolin
作者单位：Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; CNRS - National Institute for Mathematical Sciences (INSMI); Centre National de la Recherche Scientifique (CNRS); New York University; NYU Shanghai; Tel Aviv University; Universite PSL; Universite Paris-Dauphine; New York University; NYU Shanghai
摘要：We introduce a new exponential family of probability distributions, which can be viewed as a multivariate generalization of the inverse Gaussian distribution. Considered as the potential of a random Schrodinger operator, this exponential family is related to the random field that gives the mixing measure of the Vertex Reinforced Jump Process (VRJP), and hence to the mixing measure of the Edge Reinforced Random Walk (ERRW), the so-called magic formula. In particular, it yields by direct computa...
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作者：Flint, Ian; Torrisi, Giovanni Luca
作者单位：Nanyang Technological University; Consiglio Nazionale delle Ricerche (CNR); Istituto per le Applicazioni del Calcolo Mauro Picone (IAC-CNR)
摘要：We provide a Clark-Ocone formula for square-integrable functionals of a general temporal point process satisfying only a mild moment condition, generalizing known results on the Poisson space. Some classical applications are given, namely a deviation bound and the construction of a hedging portfolio in a pure-jump market model. As a more modern application, we provide a bound on the total variation distance between two temporal point processes, improving in some sense a recent result in this d...
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作者：Freidlin, M.; Koralov, L.; Wentzell, A.
作者单位：University System of Maryland; University of Maryland College Park; Tulane University
摘要：We consider processes that coincide with a given diffusion process outside a finite collection of domains. In each of the domains, there is, additionally, a large drift directed towards the interior of the domain. We describe the limiting behavior of the processes as the magnitude of the drift tends to infinity, and thus the domains become trapping, with the time to exit the domains being exponentially large. In particular, in exponential time scales, metastable distributions between the trapp...
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作者：Bhamidi, Shankar; van der Hofstad, Remco; Hooghiemstra, Gerard
作者单位：University of North Carolina; University of North Carolina Chapel Hill; Eindhoven University of Technology; Delft University of Technology
摘要：We consider first passage percolation on the configuration model with n vertices, and general independent and identically distributed edge weights assumed to have a density. Assuming that the degree distribution satisfies a uniform X-2 log X-condition, we analyze the asymptotic distribution for the minimal weight path between a pair of typical vertices, as well the number of edges on this path namely the hopcount. Writing L-n for the weight of the optimal path, we show that Ln (log n)/alpha(n)...
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作者：Chernozhukov, Victor; Chetverikov, Denis; Kato, Kengo
作者单位：Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT); University of California System; University of California Los Angeles; University of Tokyo
摘要：This paper derives central limit and bootstrap theorems for probabilities that sums of centered high-dimensional random vectors hit hyperrectangles and sparsely convex sets. Specifically, we derive Gaussian and bootstrap approximations for probabilities P(n(-1/2) Sigma(n)(i=1) X-i is an element of A) where X-1,...,X-n are independent random vectors in R-p and A is a hyperrectangle, or more generally, a sparsely convex set, and show that the approximation error converges to zero even if p = p(n...
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作者：Dereich, Steffen; Doring, Leif; Kyprianou, Andreas E.
作者单位：University of Munster; University of Mannheim; University of Bath
摘要：Since the seminal work of Lamperti, there is a lot of interest in the understanding of the general structure of self-similar Markov processes. Lamperti gave a representation of positive self-similar Markov processes with initial condition strictly larger than 0 which subsequently was extended to zero initial condition. For real self-sinfilar Markov processes (rssMps), there is a generalization of Lamperti's representation giving a one-to-one correspondence between Markov additive processes and...
