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作者：Chen, Lung-Chi; Sakai, Akira
作者单位：Fu Jen Catholic University; Hokkaido University
摘要：We consider long-range self-avoiding walk, percolation and the Ising model on Z(d) that are defined by power-law decaying pair potentials of the form D(x) asymptotic to vertical bar x vertical bar(-d-alpha) with alpha > 0. The upper-critical dimension d(c) is 2(alpha boolean AND 2) for self-avoiding walk and the Ising model, and 3(alpha boolean AND 2) for percolation. Let alpha not equal 2 and assume certain heat-kernel bounds on the n-step distribution of the underlying random walk. We prove ...
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作者：Dembo, Amir; Mukherjee, Sumit
作者单位：Stanford University; Stanford University
摘要：Consider random polynomial Sigma(n)(i=0) a(i)x(i) of independent mean-zero normal coefficients a(i), whose variance is a regularly varying function (in i) of order alpha. We derive general criteria for continuity of persistence exponents for centered Gaussian processes, and use these to show that such polynomial has no roots in [0, 1] with probability n(-b alpha+o(1)), and no roots in (1, infinity) with probability n(-b0+o(1)), hence for n even, it has no real roots with probability n(-2b alph...
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作者：Le Jan, Yves; Marcus, Michael B.; Rosen, Jay
作者单位：Universite Paris Saclay; City University of New York (CUNY) System; City College of New York (CUNY); City University of New York (CUNY) System; College of Staten Island (CUNY)
摘要：A permanental field, psi = {psi(v), v is an element of V}, is a particular stochastic process indexed by a space of measures on a set S. It is determined by a kernel u(x, y), x, y is an element of S, that need not be symmetric and is allowed to be infinite on the diagonal. We show that these fields exist when u (x, y) is a potential density of a transient Markov process X in S. A permanental field psi can be realized as the limit of a renormalized sum of continuous additive functionals determi...
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作者：Foss, Sergey; Rolla, Leonardo T.; Sidoravicius, Vladas
作者单位：Heriot Watt University; University of Buenos Aires
摘要：We consider a self-interacting process described in terms of a single-server system with service stations at each point of the real line. The customer arrivals are given by a Poisson point processes on the space time half plane. The server adopts a greedy routing mechanism, traveling toward the nearest customer, and ignoring new arrivals while in transit. We study the trajectories of the server and show that its asymptotic position diverges logarithmically in time.
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作者：Chen, Yu-Ting
作者单位：Harvard University
摘要：We prove pathwise nonuniqueness in the stochastic partial differential equations (SPDEs) for some one-dimensional super-Brownian motions with immigration. In contrast to a closely related case investigated by Mueller, Mytnik and Perkins [Ann. Probab. 42 (2014) 2032-21121, the solutions of the present SPDEs are assumed to be nonnegative and have very different properties including uniqueness in law. In proving possible separation of solutions, we derive delicate properties of certain correlated...
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作者：Kleptsyn, Victor; Kurtzmann, Aline
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Rennes; Universite de Lorraine; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Lorraine; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：In this paper, we construct a counterexample to a question by Cantelli, asking whether there exists a nonconstant positive measurable function phi such that for i.i.d. r.v. X, Y of law N(0, 1), the r.v. X + phi(X) . Y is also Gaussian. This construction is made by finding an unusual solution to the Skorokhod embedding problem (showing that the corresponding Brownian transport, contrary to the Root barrier, is not unique). To find it, we establish some sufficient conditions for the continuity o...
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作者：Kharroubi, Idris; Huyen Pham
作者单位：Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite; Institut Polytechnique de Paris; ENSAE Paris
摘要：We aim to provide a Feynman-Kac type representation for Hamilton Jacobi-Bellman equation, in terms of forward backward stochastic differential equation (FBSDE) with a simulatable forward process. For this purpose, we introduce a class of BSDE where the jumps component of the solution is subject to a partial nonpositive constraint. Existence and approximation of a unique minimal solution is proved by a penalization method under mild assumptions. We then show how minimal solution to this BSDE cl...
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作者：Georgiou, Nicos; Rassoul-Agha, Firas; Seppaelaeinen, Timo; Yilmaz, Atilla
作者单位：University of Sussex; Utah System of Higher Education; University of Utah; University of Wisconsin System; University of Wisconsin Madison; Bogazici University
摘要：We introduce a random walk in random environment associated to an underlying directed polymer model in 1 + 1 dimensions. This walk is the positive temperature counterpart of the competition interface of percolation and arises as the limit of quenched polymer measures. We prove this limit for the exactly solvable log-gamma polymer, as a consequence of almost sure limits of ratios of partition functions. These limits of ratios give the Busemann functions of the log-gamma polymer, and furnish cen...
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作者：Berestycki, Nathanael; Garban, Christophe; Sen, Arnab
作者单位：University of Cambridge; 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; University of Minnesota System; University of Minnesota Twin Cities
摘要：The coalescing Brownian flow on R is a process which was introduced by Arratia [Coalescing Brownian motions on the line (1979) Univ. Wisconsin, Madison] and Toth and Werner [Probab. Theory Related Fields 111 (1998) 375-452], and which formally corresponds to starting coalescing Brownian motions from every space-time point. We provide a new state space and topology for this process and obtain an invariance principle for coalescing random walks. This result holds under a finite variance assumpti...
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作者：Khoshnevisan, Davar; Kim, Kunwoo
作者单位：Utah System of Higher Education; University of Utah
摘要：Consider the stochastic heat equation partial derivative(t)u = Lu + lambda sigma (u)xi, where L denotes the generator of a Levy process on a locally compact Hausdorff Abelian group G, sigma : R -> R is Lipschitz continuous, lambda >> 1 is a large parameter, and xi denotes space time white noise on R+ x G. The main result of this paper contains a near-dichotomy for the (expected squared) energy E(parallel to u(t)parallel to(2)(L2(G))) of the solution. Roughly speaking, that dichotomy says that,...
