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作者：Bai, Shuyang; Taqqu, Murad S.
作者单位：Boston University
摘要：The generalized Rosenblatt process is obtained by replacing the single critical exponent characterizing the Rosenblatt process by two different exponents living in the interior of a triangular region. What happens to that generalized Rosenblatt process as these critical exponents approach the boundaries of the triangle? We show by two different methods that on each of the two symmetric boundaries, the limit is non-Gaussian. On the third boundary, the limit is Brownian motion. The rates of conv...
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作者：Adler, Robert J.; Samorodnitsky, Gennady
作者单位：Technion Israel Institute of Technology; Cornell University
摘要：How likely is the high level of a continuous Gaussian random field on an Euclidean space to have a hole of a certain dimension and depth? Questions of this type are difficult, but in this paper we make progress on questions shedding new light in existence of holes. How likely is the field to be above a high level on one compact set (e.g., a sphere) and to be below a fraction of that level on some other compact set, for example, at the center of the corresponding ball? How likely is the field t...
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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：Kemppainen, Antti; Smirnov, Stanislav
作者单位：University of Helsinki; University of Geneva
摘要：In this paper, we provide a framework of estimates for describing 2D scaling limits by Schramm's SLE curves. In particular, we show that a weak estimate on the probability of an annulus crossing implies that a random curve arising from a statistical mechanics model will have scaling limits and those will be well described by Loewner evolutions with random driving forces. Interestingly, our proofs indicate that existence of a nondegenerate observable with a conformally- invariant scaling limit ...
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作者：Kassel, Adrien; Kenyon, Richard
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; Brown University
摘要：We define natural probability measures on finite multicurves (finite collections of pairwise disjoint simple closed curves) on curved surfaces. These measures arise as universal scaling limits of probability measures on cyclerooted spanning forests (CRSFs) on graphs embedded on a surface with a Riemannian metric, in the limit as the mesh size tends to zero. These in turn are defined from the Laplacian determinant and depend on the choice of a unitary connection on the surface. Wilson's algorit...
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作者：Buckdahn, Rainer; Li, Juan; Peng, Shige; Rainer, Catherine
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Bretagne Occidentale; Shandong University; Shandong University
摘要：In this paper we consider a mean-field stochastic differential equation, also called Mc Kean-Vlasov equation, with initial data (t,x)is an element of[0,T]xR(d), which coefficients depend on both the solution X-s(t,x) but also its law. By considering square integrable random variables xi as initial condition for this equation, we can easily show the flow property of the solution X-s(t,xi) of this new equation. Associating it with a process X-s(t,x,P xi) which coincides with X-s(t,xi), when one ...
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作者：Martineau, Sebastien; Tassion, Vincent
作者单位：Weizmann Institute of Science; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We prove that the value of the critical probability for percolation on an Abelian Cayley graph is determined by its local structure. This is a partial positive answer to a conjecture of Schramm: the function pc defined on the set of Cayley graphs of Abelian groups of rank at least 2 is continuous for the Benjamini-Schramm topology. The proof involves group-theoretic tools and a new block argument.
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作者：Athreya, Siva; Loehr, Wolfgang; Winter, Anita
作者单位：Indian Statistical Institute; Indian Statistical Institute Bangalore; University of Duisburg Essen
摘要：We consider stochastic processes on complete, locally compact tree-like metric spaces (T,r) on their natural scale with boundedly finite speed measure ?. Given a triple (T,r,nu) such a speed-nu motion on (T,r) can be characterized as the unique strong Markov process which if restricted to compact subtrees satisfies for all x,y is an element of T and all positive, bounded measurable f, E-x[integral(tau y)(0)dsf(X-s)]=2 integral(T)nu(dz)r(y,c(x,y,z))f(z)
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作者：Barchiesi, Marco; Brancolini, Alessio; Julin, Vesa
作者单位：University of Naples Federico II; University of Munster; University of Jyvaskyla
摘要：We provide a full quantitative version of the Gaussian isoperimetric inequality: the difference between the Gaussian perimeter of a given set and a half- space with the same mass controls the gap between the norms of the corresponding barycenters. In particular, it controls the Gaussian measure of the symmetric difference between the set and the half- space oriented so to have the barycenter in the same direction of the set. Our estimate is independent of the dimension, sharp on the decay rate...
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作者：Bally, Vlad; Caramellino, Lucia
作者单位：Inria; Centre National de la Recherche Scientifique (CNRS); Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); University of Rome Tor Vergata
摘要：Fournier and Printems [Bernoulli 16 (2010) 343-360] have recently established a methodology which allows to prove the absolute continuity of the law of the solution of some stochastic equations with Holder continuous coefficients. This is of course out of reach by using already classical probabilistic methods based on Malliavin calculus. By employing some Besov space techniques, Debussche and Romito [Probab. Theory Related Fields 158 (2014) 575-596] have substantially improved the result of Fo...
