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作者：Athreya, Siva; Joseph, Mathew; Mueller, Carl
作者单位：Indian Statistical Institute; Indian Statistical Institute Kolkata; University of Rochester
摘要：We consider the following stochastic partial differential equation on t >= 0, x is an element of [0, J], J >= 1, where we consider [0, J] to be the circle with end points identified, partial derivative(t)u(t, x) = 1/2 partial derivative(2)(x) u(t, x) + g(t, x, u) + sigma(t, x, u) (W) over dot (t, x), (W) over dot (t, x) is 2-parameter d-dimensional vector valued white noise and sigma is function from R+ x R x R-d to space of symmetric d x d matrices which is Lipschitz in u. We assume that sigm...
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作者：Galashin, Pavel
作者单位：University of California System; University of California Los Angeles
摘要：We discover a new property of the stochastic colored six-vertex model called flip-invariance. We use it to show that for a given collection of observables of the model, any transformation that preserves the distribution of each individual observable also preserves their joint distribution. This generalizes recent shift-invariance results of Borodin-Gorin-Wheeler. As limiting cases, we obtain similar statements for the Brownian last passage percolation, the Kardar-Parisi-Zhang equation, the Air...
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作者：Thevenin, Paul
作者单位：Uppsala University
摘要：We provide a new geometric representation of a family of fragmentation processes by nested laminations which are compact subsets of the unit disk made of noncrossing chords. We specifically consider a fragmentation, obtained by cutting a random stable tree at random points, which split the tree into smaller subtrees. When coding each of these cutpoints by a chord in the unit disk, we separate the disk into smaller connected components, corresponding to the smaller subtrees of the initial tree....
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作者：Hartarsky, Ivailo; Martinelli, Fabio; Toninelli, Cristina
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite PSL; Universite Paris-Dauphine; Roma Tre University
摘要：In this paper, we consider kinetically constrained models (KCM) on Z(2) with general update families U. For U belonging to the so-called critical class, our focus is on the divergence of the infection time of the origin for the equilibrium process as the density of the facilitating sites vanishes. In a recent paper (Probab. Theory Related Fields 178 (2020) 289-326), Mareche and two of the present authors proved that if U has an infinite number of stable directions, then on a doubly logarithmic...
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作者：Salins, Michael; Spiliopoulos, Konstantinos
作者单位：Boston University
摘要：In this paper we develop a metastability theory for a class of stochastic reaction-diffusion equations exposed to small multiplicative noise. We consider the case where the unperturbed reaction-diffusion equation features multiple asymptotically stable equilibria. When the system is exposed to small stochastic perturbations, it is likely to stay near one equilibrium for a long period of time but will eventually transition to the neighborhood of another equilibrium. We are interested in studyin...
