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作者：Harangi, Viktor; Virag, Balint
作者单位：University of Toronto
摘要：A theorem of Hoffman gives an upper bound on the independence ratio of regular graphs in terms of the minimum lambda(min) of the spectrum of the adjacency matrix. To complement this result we use random eigenvectors to gain lower bounds in the vertex-transitive case. For example, we prove that the independence ratio of a 3-regular transitive graph is at least q = 1/2 - 3/4 pi arccos (1-lambda(min)/4). The same bound holds for infinite transitive graphs: we construct factor of i.i.d. independen...
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作者：Lyons, Terry; Ni, Hao
作者单位：University of Oxford
摘要：The signature of a path provides a top down description of the path in terms of its effects as a control [Differential Equations Driven by Rough Paths (2007) Springer]. The signature transforms a path into a group-like element in the tensor algebra and is an essential object in rough path theory. The expected signature of a stochastic process plays a similar role to that played by the characteristic function of a random variable. In [Chevyrev (2013)], it is proved that under certain boundednes...
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作者：Brofferio, Sara; Buraczewski, Dariusz
作者单位：Universite Paris Saclay; Universite Paris Saclay; University of Wroclaw
摘要：We consider stochastic dynamical systems on R, that is, random processes defined by X-n(x) = Psi(n)(X-n-1(x)), X-0(x) = x, where Psi(n) are i.i.d. random continuous transformations of some unbounded closed subset of R. We assume here that Psi(n) behaves asymptotically like A(n)x, for some random positive number A(n) [the main example is the affine stochastic recursion Psi(n) (x) = A(n)x + B-n]. Our aim is to describe invariant Radon measures of the process X-n(x) in the critical case, when E l...
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作者：Dupuis, Paul; Liu, Yufei
作者单位：Brown University; Alphabet Inc.; Google Incorporated
摘要：The large deviations principle for the empirical measure for both continuous and discrete time Markov processes is well known. Various expressions are available for the rate function, but these expressions are usually as the solution to a variational problem, and in this sense not explicit. An interesting class of continuous time, reversible processes was identified in the original work of Donsker and Varadhan for which an explicit expression is possible. While this class includes many (revers...
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作者：Camia, Federico; Garban, Christophe; Newman, Charles M.
作者单位：Vrije Universiteit Amsterdam; New York University; New York University Abu Dhabi; Centre National de la Recherche Scientifique (CNRS); Ecole Normale Superieure de Lyon (ENS de LYON); New York University; Vrije Universiteit Amsterdam; University of California System; University of California Irvine
摘要：The aim of this paper is to prove the following result. Consider the critical Ising model on the resealed grid aZ(2), then the renormalized magnetization field Phi(a) := a(15/8)s Sigma(x is an element of aZ2)sigma(x)delta(x), seen as a random distribution (i.e., generalized function) on the plane, has a unique scaling limit as the mesh size a SE arrow 0. The limiting field is conformally covariant.
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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...
