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作者：Kious, Daniel; Sidoravicius, Vladas
作者单位：New York University; New York University; NYU Shanghai
摘要：In this short paper, we consider the Once-reinforced random walk with reinforcement parameter a on trees with bounded degree which are transient for the simple random walk. On each of these trees, we prove that there exists an explicit critical parameter a(0) such that the Once-reinforced random walk is almost surely recurrent if a > a(0) and almost surely transient if a < a(0). This provides the first examples of phase transition for the Once-reinforced random walk.
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作者：Barbu, Viorel; Roeckner, Michael; Zhang, Deng
作者单位：Romanian Academy; Alexandru Ioan Cuza University; University of Bielefeld; Shanghai Jiao Tong University
摘要：We analyze the bilinear optimal control problem of quantum mechanical systems with final observation governed by a stochastic nonlinear Schrodinger equation perturbed by a linear multiplicative Wiener process. The existence of an open-loop optimal control and first-order Lagrange optimality conditions are derived, via Skorohod's representation theorem, Ekeland's variational principle and the existence for the linearized dual backward stochastic equation. Moreover, our approach in particular ap...
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作者：Stauffer, Alexandre; Taggi, Lorenzo
作者单位：University of Bath; Technical University of Darmstadt
摘要：We consider the activated random walk model on general vertex-transitive graphs. A central question in this model is whether the critical density mu(c) for sustained activity is strictly between 0 and 1. It was known that mu c > 0 on Z(d), d >= 1, and that mu(c) < 1 on Z for small enough sleeping rate. We show that mu(c) -> 0 as lambda -> 0 in all vertex-transitive transient graphs, implying that mu(c) < 1 for small enough sleeping rate. We also show that mu(c) < 1 for any sleeping rate in any...
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作者：Bassino, Frederique; Bouvel, Mathilde; Feray, Valentin; Gerin, Lucas; Pierrot, Adeline
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - Institute for Information Sciences & Technologies (INS2I); Universite Paris 13; University of Zurich; Institut Polytechnique de Paris; Ecole Polytechnique; Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS)
摘要：We study uniform random permutations in an important class of pattern-avoiding permutations: the separable permutations. We describe the asymptotics of the number of occurrences of any fixed given pattern in such a random permutation in terms of the Brownian excursion. In the recent terminology of permutons, our work can be interpreted as the convergence of uniform random separable permutations towards a Brownian separable permuton.
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作者：Grama, Ion; Lauvergnat, Ronan; Le Page, Emile
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：Consider a Markov chain (X-n)(n >= 0) with values in the state space X. Let f be a real function on X and set S-n = Sigma(n)(i=1) f(X-i), n >= 1. Let P-x be the probability measure generated by the Markov chain starting at X-0 = x. For a starting point y is an element of R, denote by tau(y) the first moment when the Markov walk (y + S-n)(n >= 1) becomes nonpositive. Under the condition that S-n has zero drift, we find the asymptotics of the probability P-x (tau(y) > n) and of the conditional l...
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作者：Seo, Insuk
作者单位：Seoul National University (SNU)
摘要：This paper presents our study of the asymptotic behavior of a two-component system of Brownian motions undergoing certain form of singular interactions. In particular, the system is a combination of two different types of particles and the mechanical properties and the interaction parameters depend on the corresponding type of particles. We prove that the hydrodynamic limit of the empirical densities of two types is the solution of a partial differential equation known as the Maxwell-Stefan eq...
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作者：Collamore, Jeffrey F.; Mentemeier, Sebastian
作者单位：University of Copenhagen; Dortmund University of Technology; Dortmund University of Technology
摘要：We study the large exceedance probabilities and large exceedance paths of the recursive sequence V-n = MnVn-1 + Q(n), where {(M-n, Q(n))} is an i.i.d. sequence, and M-1 is a d x d random matrix and Q(1) is a random vector, both with nonnegative entries. We impose conditions which guarantee the existence of a unique stationary distribution for {V-n} and a Cramr-type condition for {M-n}. Under these assumptions, we characterize the distribution of the first passage time T-u(A) = inf{n : V-n is a...
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作者：Lyons, Russell
作者单位：Indiana University System; Indiana University Bloomington
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作者：Benjamini, Itai; Paquette, Elliot; Pfeffer, Joshua
作者单位：Weizmann Institute of Science; University System of Ohio; Ohio State University; Massachusetts Institute of Technology (MIT)
摘要：We show that a random walk on a stationary random graph with positive anchored expansion and exponential volume growth has positive speed. We also show that two families of random triangulations of the hyperbolic plane, the hyperbolic Poisson-Voronoi tessellation and the hyperbolic Poisson-Delaunay triangulation, have 1-skeletons with positive anchored expansion. As a consequence, we show that the simple random walks on these graphs have positive hyperbolic speed. Finally, we include a section...
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作者：Gorin, Vadim; Shkolnikov, Mykhaylo
作者单位：Massachusetts Institute of Technology (MIT); Kharkevich Institute for Information Transmission Problems of the RAS; Russian Academy of Sciences; Princeton University
摘要：We determine the operator limit for large powers of random symmetric tridiagonal matrices as the size of the matrix grows. The result provides a novel expression in terms of functionals of Brownian motions for the Laplace transform of the Airy beta process, which describes the largest eigen-values in the beta ensembles of random matrix theory. Another consequence is a Feynman-Kac formula for the stochastic Airy operator of Edelman-Sutton and Ramirez-Rider-Virag. As a side result, we find that ...
