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作者：Kyprianou, Andreas E.; Carlos Pardo, Juan; Watson, Alexander R.
作者单位：University of Bath; CIMAT - Centro de Investigacion en Matematicas
摘要：We consider two first passage problems for stable processes, not necessarily symmetric, in one dimension. We make use of a novel method of path. censoring in order to deduce explicit formulas for hitting probabilities, hitting distributions and a killed potential measure. To do this, we describe in full detail the Wiener-Hopf factorization of a new Lamperti-stable-type Levy process obtained via the Lamperti transform, in the style of recent work in this area.
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作者：Li, Zenghu
作者单位：Beijing Normal University
摘要：A family of continuous-state branching processes with immigration are constructed as the solution flow of a stochastic equation system driven by time space noises. The family can be regarded as an inhomogeneous increasing path-valued branching process with immigration. Two nonlocal branching immigration superprocesses can be defined from the flow. We identify explicitly the branching and immigration mechanisms of those processes. The results provide new perspectives into the tree-valued Markov...
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作者：Kabluchko, Zakhar; Zaporozhets, Dmitry
作者单位：Ulm University; Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences; St. Petersburg Department of the Steklov Mathematical Institute of the Russian Academy of Sciences
摘要：Let xi(0), xi(1,) . . . be independent identically distributed complex-valued random variables such that E log(1 + vertical bar xi(0)vertical bar) < infinity. We consider random analytic functions of the form G(n)(z) = Sigma xi(k)f(k,n)Z(k), where f(k,n) are deterministic complex coefficients. Let mu(n) be the random measure counting the complex zeros of G(n) according to their multiplicities. Assuming essentially that -1/nlog f([tn]),(n) -> u(t) as n -> infinity, where u(t) is some function, ...
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作者：Gess, Benjamin
作者单位：Humboldt University of Berlin
摘要：Unique existence of solutions to porous media equations driven by continuous linear multiplicative space time rough signals is proven for initial data in L-1(O) on bounded domains O. The generation of a continuous, order-preserving random dynamical system on L-1(O) and the existence of a random attractor for stochastic porous media equations perturbed by linear multiplicative noise in space and time is obtained. The random attractor is shown to be compact and attracting in L-infinity(O) norm. ...
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作者：Bordenave, Charles; Caputo, Pietro
作者单位：Universite Federale Toulouse Midi-Pyrenees (ComUE); Universite de Toulouse; Institut National des Sciences Appliquees de Toulouse; Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Roma Tre University
摘要：We consider n x n Hermitian matrices with i.i.d. entries X-ij whose tail probabilities P(vertical bar X-ij vertical bar >= t) behave like e(-at alpha) for some a > 0 and alpha is an element of (0, 2). We establish a large deviation principle for the empirical spectral measure of X/root n with speed n(1+alpha/2) with a good rate function J(mu) that is finite only if mu is of the form mu = mu(sc) boxed plus nu for some probability measure nu on R, where boxed plus denotes the free convolution an...
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作者：Da Prato, Giuseppe; Lunardi, Alessandra
作者单位：Scuola Normale Superiore di Pisa; University of Parma
摘要：We consider an elliptic Kolmogorov equation lambda u - Ku = f in a separable Hilbert space H. The Kolmogorov operator K is associated to an infinite dimensional convex gradient system: dX = (AX - DU (X)) dt + dW (t), where A is a self-adjoint operator in H, and U is a convex lower semicontinuous function. Under mild assumptions we prove that for lambda > 0 and f is an element of L-2(H, v) the weak solution u belongs to the Sobolev space W-2,W-2 (H, v), where v is the log-concave probability me...
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作者：Duplantier, Bertrand; Rhodes, Remi; Sheffield, Scott; Vargas, Vincent
作者单位：Universite Paris Saclay; CEA; Centre National de la Recherche Scientifique (CNRS); Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS); CNRS - Institute of Chemistry (INC); Massachusetts Institute of Technology (MIT)
摘要：In this paper, we study Gaussian multiplicative chaos in the critical case. We show that the so-called derivative martingale, introduced in the context of branching Brownian motions and branching random walks, converges almost surely (in all dimensions) to a random measure with full support. We also show that the limiting measure has no atom. In connection with the derivative martingale, we write explicit conjectures about the glassy phase of log-correlated Gaussian potentials and the relation...
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作者：Aidekon, Elie; Shi, Zhan
作者单位：Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We consider the boundary case (in the sense of Biggins and Kyprianou [Electron. J. Probab. 10 (2005) 609-631] in a one-dimensional supercritical branching random walk, and study the additive martingale (W-n). We prove that, upon the system's survival, n(1/2)W(n) converges in probability, but not almost surely, to a positive limit. The limit is identified as a constant multiple of the almost sure limit, discovered by Biggins and Kyprianou, of the derivative martingale.
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作者：Andjel, E. D.
作者单位：Aix-Marseille Universite
摘要：We study subcritical two-dimensional oriented percolation seen from its rightmost point on the set of infinite configurations which are bounded above. This a Feller process whose state space is not compact and has no invariant measures. We prove that it converges in distribution to a measure which charges only finite configurations.
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作者：Armstrong, Scott N.; Smart, Charles K.
作者单位：University of Wisconsin System; University of Wisconsin Madison; Universite PSL; Universite Paris-Dauphine; Massachusetts Institute of Technology (MIT)
摘要：We prove regularity and stochastic homogenization results for certain degenerate elliptic equations in nondivergence form. The equation is required to be strictly elliptic, but the ellipticity may oscillate on the microscopic scale and is only assumed to have a finite dth moment, where d is the dimension. In the general stationary-ergodic framework, we show that the equation homogenizes to a deterministic, uniformly elliptic equation, and we obtain an explicit estimate of the effective ellipti...
