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作者：Marcus, Michael B.; Rosen, Jay
作者单位：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：An alpha-permanental process {X-t, t is an element of T} is a stochastic process determined by a kernel K = {K (s, t), s, t is an element of T}, with the property that for all t(1),..., t(n) is an element of T, vertical bar I + K(t(1),..., t(n)) S vertical bar(-alpha) is the Laplace transform of (X-t1,...,X-tn), where K (t(1),...,t(n)) denotes the matrix {K(t(i), t(j))}(i,j)(n) = 1 and S is the diagonal matrix with entries s(1),...,s(n). (X-t1,..., X-tn) s called a permanental vector. Under th...
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作者：Caravenna, Francesco; Toninelli, Fabio Lucid; Torri, Niccolo
作者单位：University of Milano-Bicocca; 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; Centre National de la Recherche Scientifique (CNRS); 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
摘要：We consider disordered pinning models, when the return time distribution of the underlying renewal process has a polynomial tail with exponent alpha is an element of (1/2, 1). This corresponds to a regime where disorder is known to be relevant, that is, to change the critical exponent of the localization transition and to induce a nontrivial shift of the critical point. We show that the free energy and critical curve have an explicit universal asymptotic behavior in the weak coupling regime, d...
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作者：Li, Liping; Ying, Jiangang
作者单位：Fudan University
摘要：The main purpose of this paper is to explore the structure of regular Dirichlet subspaces of one-dimensional Brownian motion. As stated in [Osaka J. Math. 42 (2005) 27-41], every such regular Dirichlet subspace can be characterized by a measure-dense set G. When G is open, F = G(c) is the boundary of G and, before leaving G, the diffusion associated with the regular Dirichlet subspace is nothing but Brownian motion. Their traces on F still inherit the inclusion relation, in other words, the tr...
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作者：Deligiannidis, George; Kosloff, Zemer
作者单位：University of Oxford; University of Warwick
摘要：We answer a question of Aaronson about the relative complexity of Random Walks in Random Sceneries driven by either aperiodic two-dimensional random walks, two-dimensional Simple Random walk, or by aperiodic random walks in the domain of attraction of the Cauchy distribution. A key step is proving that the range of the random walk satisfies the Folner property almost surely.
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作者：Mourrat, Jean-Christophe; Weber, Hendrik
作者单位：Ecole Normale Superieure de Lyon (ENS de LYON); University of Warwick
摘要：We show global well-posedness of the dynamic Phi(4) model in the plane. The model is a nonlinear stochastic PDE that can only be interpreted in a renormalised sense. Solutions take values in suitable weighted Besov spaces of negative regularity.
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作者：Foondun, Mohammud; Liu, Wei; Omaba, Mcsylvester
作者单位：University of Strathclyde; Shanghai Normal University
摘要：We consider fractional stochastic heat equations of the form partial derivative u(t)(x)/partial derivative t = -(-Delta)(alpha/2)u(t)(x) + lambda sigma(u(t)(x))(F) over dot (t, x). Here, (F) over dot denotes the noise term. Under suitable assumptions, we show that the second moment of the solution grows exponentially with time. Since we do not assume that the initial condition is bounded below, this solves an open problem stated in [Probab. Theory Related Fields 152 (2012) 681-701]. Along the ...
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作者：Hough, Bob; Jiang, Yunjiang
作者单位：Stanford University
摘要：We consider an analogue of the Kac random walk on the special orthogonal group SO(N), in which at each step a random rotation is performed in a randomly chosen 2-plane of R-N. We obtain sharp asymptotics for the rate of convergence in total variance distance, establishing a cut-off phenomenon in the large N limit. In the special case where the angle of rotation is deterministic, this confirms a conjecture of Rosenthal [Ann. Probab. 22 (1994) 398-423]. Under mild conditions, we also establish a...
