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作者：Wu, Wei Biao
作者单位：University of Chicago
摘要：We establish strong invariance principles for sums of stationary and ergodic processes with nearly optimal bounds. Applications to linear and some nonlinear processes are discussed. Strong laws of large numbers and laws of the iterated logarithm are also obtained under easily verifiable conditions.
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作者：Broman, Erik I.
作者单位：Chalmers University of Technology
摘要：The ordinary contact process is used to model the spread of a disease in a population. In this model, each infected individual waits an exponentially distributed time with parameter 1 before becoming healthy. In this paper, we introduce and study the contact process in a randomly evolving environment. Here we associate to every individual an independent two-state, {0, 1}, background process. Given delta(0) < delta(1), if the background process is in state 0, the individual (if infected) become...
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作者：Bertoin, Jean
作者单位：Sorbonne Universite; Universite Paris Cite; Universite Paris Cite; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We consider a Langevin process with white noise random forcing. We suppose that the energy of the particle is instantaneously absorbed when it hits some fixed obstacle. We show that nonetheless, the particle can be instantaneously reflected, and study some properties of this reflecting solution.
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作者：Guionnet, Alice; Maurel-Segala, Edouard
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Ecole Normale Superieure de Lyon (ENS de LYON)
摘要：We study several-matrix models and show that when the potential is convex and a small perturbation of the Gaussian potential, the first order correction to the free energy can be expressed as a generating function for the enumeration of maps of genus one. In order to do that, we prove a central limit theorem for traces of words of the weakly interacting random matrices defined by these matrix models and show that the variance is a generating function for the number of planar maps with two vert...
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作者：Birkner, Matthias; Zaehle, Iljana
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; University of Erlangen Nuremberg
摘要：We show that the centred occupation time process of the origin of a system of critical binary branching random walks in dimension d >= 3, started off either from a Poisson field or in equilibrium, when suitably normalized, converges to a Brownian motion in d >= 4. In d = 3, the limit process is a fractional Brownian motion with Hurst parameter 3/4 when starting in equilibrium, and a related Gaussian process when starting from a Poisson field. For (dependent) branching random walks with state d...
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作者：Panchenko, Dmitry; Talagrand, Michel
作者单位：Massachusetts Institute of Technology (MIT); Sorbonne Universite; University System of Ohio; Ohio State University
摘要：In order to study certain questions concerning the distribution of the overlap in Sherrington-Kirkpatrick type models, such as the chaos and ultrametricity problems, it seems natural to study the free energy of multiple systems with constrained overlaps. One can write analogues of Guerra's replica symmetry breaking bound for such systems but it is not at all obvious how to choose informative functional order parameters in these bounds. We were able to make some progress for spherical pure p-sp...
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作者：Pemantle, Robin; Peres, Yuval
作者单位：University of Pennsylvania; University of California System; University of California Berkeley
摘要：We give potential theoretic estimates for the probability that a set A contains a double point of planar Brownian motion run for unit time. Unlike the probability for A to intersect the range of a Markov process, this cannot be estimated by a capacity of the set A. Instead, we introduce the notion of a capacity with respect to two gauge functions simultaneously. We also give a polar decomposition of A into a set that never intersects the set of Brownian double points and a set for which inters...
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作者：Swanson, Jason
作者单位：University of Wisconsin System; University of Wisconsin Madison
摘要：We consider the solution to a stochastic heat equation. This solution is a random function of time and space. For a fixed point in space, the resulting random function of time, F(t), has a nontrivial quartic variation. This process, therefore, has infinite quadratic variation and is not a semimartingale. It follows that the classical Ito calculus does not apply. Motivated by heuristic ideas about a possible new calculus for this process, we are led to study modifications of the quadratic varia...
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作者：Weill, Mathilde
作者单位：Universite PSL; Ecole Normale Superieure (ENS)
摘要：In this work, we give a description of all a-finite measures on the space of rooted compact R-trees which satisfy a certain regenerative property. We show that any infinite measure which satisfies the regenerative property is the law of a Levy tree, that is, the law of a tree-valued random variable that describes the genealogy of a population evolving according to a continuous-state branching process. On the other hand, we prove that a probability measure with the regenerative property must be...
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作者：Ben Arous, Gerard; Cerny, Jiri
作者单位：New York University; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
摘要：We give the quenched scaling limit of Bouchaud's trap model in d >= 2. This scaling limit is the fractional-kinetics process, that is the time change of a d-dimensional Brownian motion by the inverse of an independent alpha-stable subordinator.
