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作者：Castell, Fabienne
作者单位：Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite
摘要：Let (X(t), t >= 0) be a continuous time simple random walk on Z(d) (d >= 3), and let I(T)(x) be the time spent by (X(t), t >= 0) on the site x up to time T. We prove a large deviations principle for the q-fold self-intersection local time I(T) = Sigma(x is an element of Zd) I(T)(x)(q) in the critical case q = d/d-2. When q is integer, we obtain similar results for the intersection local times of q independent simple random walks.
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作者：Robert, Raoul; Vargas, Vincent
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：In this article, we extend the theory of multiplicative chaos for positive definite functions in R-d of the form f(x) = lambda(2) In+ R/vertical bar x vertical bar + g(r), where g is a continuous and bounded function. The construction is simpler and more general than the one defined by Kahane in [Am. Sci. Math. Quebec 9 (1985) 105-150]. As a main application, we provide a rigorous mathematical meaning to the Kolmogorov-Obukhov model of energy dissipation in a turbulent flow.
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作者：Kharroubi, Idris; Ma, Jin; Pham, Huyen; Zhang, Jianfeng
作者单位：Institut Polytechnique de Paris; ENSAE Paris; Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); University of Southern California
摘要：We consider a class of backward stochastic differential equations (BSDEs) driven by Brownian motion and Poisson random measure, and subject to constraints on the jump component. We prove the existence and uniqueness of the minimal solution for the BSDEs by using a penalization approach. Moreover, we show that under mild conditions the minimal solutions to these constrained BSDEs can be characterized as the unique viscosity solution of quasi-variational inequalities (QVIs), which leads to a pro...
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作者：Adler, Mark; Ferrari, Patrik L.; van Moerbeke, Pierre
作者单位：Brandeis University; Universite Catholique Louvain; University of Bonn
摘要：Consider n + m nonintersecting Brownian bridges, with n of them leaving from 0 at time t = -1 and returning to 0 at time t = -1, while the m remaining ones (wanderers) go from m points a(i) to m points b(i). First, we keep m fixed and we scale a(i), b(i) appropriately with n. In the large-n limit, we obtain a new Airy process with wanderers, in the neighborhood of root 2n, the approximate location of the rightmost particle in the absence of wanderers. This new process is governed by an Airy-ty...
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作者：Peccati, G.; Sole, J. L.; Taqqu, M. S.; Utzet, F.
作者单位：Universite Paris Saclay; Sorbonne Universite; Boston University; Autonomous University of Barcelona
摘要：We combine Stein's method with a version of Malliavin calculus on the Poisson space. As a result, we obtain explicit Berry-Esseen bounds in Central limit theorems (CLTs) involving multiple Wiener-Ito integrals with respect to a general Poisson measure. We provide several applications to CLTs related to Ornstein-Uhlenbeck Levy processes.
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作者：Buergisser, Peter; Cucker, Felipe; Lotz, Martin
作者单位：University of Paderborn; City University of Hong Kong; University of Oxford
摘要：This paper has two agendas. Firstly, we exhibit new results for coverage processes. Let p(n, m, alpha) be the probability that n spherical caps of angular radius alpha in S-m do not cover the whole sphere S-m. We give an exact formula for p (n, m, alpha) in the case alpha is an element of [pi/2, pi] and an upper bound for p(n, m, alpha) in the case alpha is an element of [0, pi/2] which tends to p(n, m, pi/2) when alpha -> pi/2. In the case alpha is an element of [0, pi/2] this yields upper bo...
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作者：Bjorklund, Michael
作者单位：Royal Institute of Technology
摘要：We generalize the asymptotic shape theorem in first passage percolation on Z(d) to cover the case of general semimetrics. We prove a structure theorem for equivariant semimetrics on topological groups and an extended version of the maximal inequality for Z(d)-cocycles of Boivin and Derriennic in the vector-valued case. This inequality will imply a very general form of Kingman's subadditive ergodic theorem. For certain classes of generalized first passage percolation, we prove further structure...
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作者：Klenke, Achim; Oeler, Mario
作者单位：Johannes Gutenberg University of Mainz
摘要：Dawson and Perkins [Ann. Probab. 26 (1988) 1088-1138] constructed a stochastic model of an interacting two-type population indexed by a countable site space which locally undergoes a mutually catalytic branching mechanism. In Klenke and Mytnik [Preprint (2008), arXiv:0901.0623], it is shown that as the branching rate approaches infinity, the process converges to a process that is called the infinite rate mutually catalytic branching process (IMUB). It is most conveniently characterized as the ...
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作者：Roy, Parthanil
作者单位：Michigan State University
摘要：We consider a point process sequence induced by a stationary symmetric alpha-stable (0 < alpha < 2) discrete parameter random field. It is easy to prove, following the arguments in the one-dimensional case in [Stochastic Process. Appl. 114 (2004) 191-210], that if the random field is generated by a dissipative group action then the point process sequence converges weakly to a cluster Poisson process. For the conservative case, no general result is known even in the one-dimensional case. We loo...
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作者：Bovier, Anton; den Hollander, Frank; Spitoni, Cristian
作者单位：University of Bonn; Leiden University; Leiden University - Excl LUMC
摘要：In this paper, we study metastability in large volumes at low temperatures. We consider both Ising spins subject to Glauber spin-flip dynamics and lattice gas particles subject to Kawasaki hopping dynamics. Let beta denote the inverse temperature and let Lambda(beta) subset of Z(2) be a square box with periodic boundary conditions such that lim(beta ->infinity) vertical bar Lambda(beta)vertical bar = infinity. We run the dynamics on Lambda(beta), starting from a random initial configuration wh...
