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作者：Miclo, Laurent; Patie, Pierre; Sarkar, Rohan
作者单位：Universite de Toulouse; Universite Toulouse 1 Capitole; Toulouse School of Economics; Cornell University
摘要：The first aim of this paper is to introduce a class of Markov chains on Z(+) which are discrete self-similar in the sense that their semigroups satisfy an in-variance property expressed in terms of a discrete random dilation operator. After showing that this latter property requires the chains to be upward skip-free, we first establish a gateway intertwining relation between the semigroup of such chains and the one of spectrally negative self-similar Markov pro-cesses on R+. As a by-product, w...
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作者：Liu, Zhipeng
作者单位：University of Kansas
摘要：Recently Johansson and Rahman obtained the limiting multitime distribution for the discrete polynuclear growth model (Johansson and Rahman (2019)), which is equivalent to a discrete TASEP model with step initial condition. In this paper, we obtain a finite time multipoint distribution formula of continuous TASEP with general initial conditions in the space-time plane. We evaluate the limit of this distribution function when the times go to infinity at the same speed for both step and flat init...
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作者：Ioffe, Dmitry; Ott, Sebastien; Shlosman, Senya; Velenik, Yvan
作者单位：Technion Israel Institute of Technology; Roma Tre University; University of Geneva
摘要：In this paper, we develop a detailed analysis of critical prewetting in the context of the two-dimensional Ising model. Namely, we consider a two-dimensional nearest-neighbor Ising model in a 2N x N rectangular box with a boundary condition inducing the coexistence of the + phase in the bulk and a layer of - phase along the bottom wall. The presence of an external magnetic field of intensity h = lambda/N (for some fixed lambda > 0) makes the layer of - phase unstable. For any beta > beta(c), w...
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作者：Cerrai, Sandra; Xi, Guangyu
作者单位：University System of Maryland; University of Maryland College Park
摘要：We study the validity of a Smoluchowski-Kramers approximation for a class of wave equations in a bounded domain of R-n subject to a state-dependent damping and perturbed by a multiplicative noise. We prove that in the small mass limit the solution converges to the solution of a stochastic quasilinear parabolic equation where a noise-induced extra drift is created.
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作者：Fitzgerald, Will; Tribe, Roger; Zaboronski, Oleg
作者单位：University of Manchester; University of Warwick
摘要：Motivated by the phenomenon of duality for interacting particle systems, we introduce two classes of Pfaffian kernels describing a number of Pfaf-fian point processes in the bulk and at the edge. Using the probabilistic method due to Mark Kac, we prove two Szego-type asymptotic expansion theorems for the corresponding Fredholm Pfaffians. The idea of the proof is to introduce an effective random walk with transition density determined by the Pfaffian kernel, express the logarithm of the Fredhol...
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作者：Borga, Jacopo; Maazoun, Mickael
作者单位：University of Zurich; Ecole Normale Superieure de Lyon (ENS de LYON)
摘要：Baxter permutations, plane bipolar orientations, and a specific family of walks in the nonnegative quadrant, called tandem walks, are well-known to be related to each other through several bijections. We introduce a further new family of discrete objects, called coalescent-walk processes and we relate it to the three families mentioned above. We prove joint Benjamini-Schramm convergence (both in the annealed and quenched sense) for uniform objects in the four families. Furthermore, we explicit...
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作者：Busani, Ofer; Ferrari, Patrik L.
作者单位：University of Bristol; University of Bonn
摘要：In this paper, we consider the geodesic tree in exponential last passage percolation. We show that for a large class of initial conditions around the origin, the line-to-point geodesic that terminates in a cylinder located around the point (N, N), and whose width and length are o(N-2/3) and o(N), respectively, agrees in the cylinder, with the stationary geodesic sharing the same end-point. In the case of the point-to-point model where the geodesic starts from the origin, we consider width delt...
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作者：Dyszewski, Piotr; Gantert, Nina; Johnston, Samuel G. G.; Prochno, Joscha; Schmid, Dominik
作者单位：Technical University of Munich; University of Bath; University of Passau
摘要：We study the asymptotics of the k-regular self-similar fragmentation process. For alpha > 0 and an integer k >= 2, this is the Markov process (I-t)(t >= 0) in which each I-t is a union of open subsets of [0, 1), and independently each subinterval of I-t of size u breaks into k equally sized pieces at rate u(alpha). Let k(-mt) and k(-Mt) be the respective sizes of the largest and smallest fragments in I-t. By relating (I-t)(t >= 0) to a branching random walk, we find that there exist explicit d...
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作者：Djete, Mao Fabrice; Possamai, Dylan; Tan, Xiaolu
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Swiss Federal Institutes of Technology Domain; ETH Zurich; Chinese University of Hong Kong
摘要：We study the McKean-Vlasov optimal control problem with common noise which allow the law of the control process to appear in the state dynamics under various formulations: strong and weak ones, Markovian or non-Markovian. By interpreting the controls as probability measures on an appropriate canonical space with two filtrations, we then develop the classical measurable selection, conditioning and concatenation arguments in this new context, and establish the dynamic programming principle under...
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作者：Berestycki, Julien; Brunet, Eric; Nolen, James; Penington, Sarah
作者单位：University of Oxford; Universite PSL; Ecole Normale Superieure (ENS); Universite Paris Cite; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); Duke University; University of Bath
摘要：The Brownian bees model is a branching particle system with spatial selection. It is a system of N particles which move as independent Brownian motions in Rd and independently branch at rate 1, and, crucially, at each branching event, the particle which is the furthest away from the origin is removed to keep the population size constant. In the present work we prove that, as N -> oo, the behaviour of the particle system is well approximated by the solution of a free boundary problem (which is ...
