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作者：Joseph, Mathew; Khoshnevisan, Davar; Mueller, Carl
作者单位：University of Sheffield; Utah System of Higher Education; University of Utah; University of Rochester
摘要：We consider a system of interacting diffusions on the integer lattice. By letting the mesh size go to zero and by using a suitable scaling, we show that the system converges (in a strong sense) to a solution of the stochastic heat equation on the real line. As a consequence, we obtain comparison inequalities for product moments of the stochastic heat equation with different nonlinearities.
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作者：Kyprianou, Andreas E.; Pagett, Steven W.; Rogers, Tim; Schweinsberg, Jason
作者单位：University of Bath; University of California System; University of California San Diego
摘要：An important property of Kingman's coalescent is that, starting from a state with an infinite number of blocks, over any positive time horizon, it transitions into an almost surely finite number of blocks. This is known as coming down from infinity. Moreover, of the many different (exchangeable) stochastic coalescent models, Kingman's coalescent is the fastest to come down from infinity. In this article, we study what happens when we counteract this fastest coalescent with the action of an ext...
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作者：van der Hofstad, Remco; Holmes, Mark; Perkins, Edwin A.
作者单位：Eindhoven University of Technology; University of Auckland; University of British Columbia
摘要：We give a sufficient condition for tightness for convergence of rescaled critical spatial structures to the canonical measure of super-Brownian motion. This condition is formulated in terms of the r-point functions for r = 2,..., 5. The r-point functions describe the expected number of particles at given times and spatial locations, and have been investigated in the literature for many high-dimensional statistical physics models, such as oriented percolation and the contact process above 4 dim...
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作者：Holroyd, Alexander E.; Schramm, Oded; Wilson, David B.
作者单位：Microsoft
摘要：Suppose that the vertices of Z(d) are assigned random colors via a finitary factor of independent identically distributed (i.i.d.) vertex-labels. That is, the color of vertex v is determined by a rule that examines the labels within a finite (but random and perhaps unbounded) distance R of v, and the same rule applies at all vertices. We investigate the tail behavior of R if the coloring is required to be proper (i.e., if adjacent vertices must receive different colors). When d >= 2, the optim...
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作者：Konarovskyi, Vitalii
作者单位：Max Planck Society; Ministry of Education & Science of Ukraine; Yuri Fedkovych Chernivtsi National University
摘要：We construct a modified Arratia flow with mass and energy conservation. We suppose that particles have a mass obeying the conservation law, and their diffusion is inversely proportional to the mass. Our main result asserts that such a system exists under the assumption of the uniform mass distribution on an interval at the starting moment. We introduce a stochastic integral with respect to such a flow and obtain the total local time as the density of the occupation measure for all particles.
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作者：Basu, Riddhipratim; Hermon, Jonathan; Peres, Yuval
作者单位：Stanford University; University of California System; University of California Berkeley; Microsoft
摘要：A sequence of Markov chains is said to exhibit (total variation) cutoff if the convergence to stationarity in total variation distance is abrupt. We consider reversible lazy chains. We prove a necessary and sufficient condition for the occurrence of the cutoff phenomena in terms of concentration of hitting time of worst (in some sense) sets of stationary measure at least a, for some alpha is an element of(0,1). We also give general bounds on the total variation distance of a reversible chain a...
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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：Comets, Francis; Popov, Serguei
作者单位：Universite Paris Cite; Universidade Estadual de Campinas; Universite Paris Cite; Universidade Estadual de Campinas
摘要：For the model of two-dimensional random interlacements in the critical regime (i.e., alpha = 1), we prove that the vacant set is a.s. infinite, thus solving an open problem from [Commun. Math. Phys. 343 (2016) 129-164]. Also, we prove that the entrance measure of simple random walk on annular domains has certain regularity properties; this result is useful when dealing with soft local times for excursion processes.
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作者：Khare, Apoorva; Rajaratnam, Bala
作者单位：Stanford University; University of California System; University of California Davis; University of Sydney; Indian Institute of Science (IISC) - Bangalore
摘要：We prove a refinement of the inequality by Hoffmann-Jorgensen that is significant for three reasons. First, our result improves on the state-of-the-art even for real-valued random variables. Second, the result unifies several versions in the Banach space literature, including those by Johnson and Schechtman [Ann. Probab. 17 (1989) 789-808], Klass and Nowicki [Ann. Probab. 28 (2000) 851-862], and Hitczenko and Montgomery-Smith [Ann. Probab. 29 (2001) 447-466]. Finally, we show that the Hoffmann...
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作者：Letizia, Viviana; Olla, Stefano
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite PSL; Universite Paris-Dauphine
摘要：We consider a chain of anharmonic oscillators immersed in a heat bath with a temperature gradient and a time-varying tension applied to one end of the chain while the other side is fixed to a point. We prove that under diffusive space-time rescaling the volume strain distribution of the chain evolves following a nonlinear diffusive equation. The stationary states of the dynamics are of nonequilibrium and have a positive entropy production, so the classical relative entropy methods cannot be us...
