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作者：Hammer, Matthias; Ortgiese, Marcel; Vollering, Florian
作者单位：Technical University of Berlin; University of Bath
摘要：The symbiotic branching model is a spatial population model describing the dynamics of two interacting types that can only branch if both types are present. A classical result for the underlying stochastic partial differential equation identifies moments of the solution via a duality to a system of Brownian motions with dynamically changing colors. In this paper, we revisit this duality and give it a new interpretation. This new approach allows us to extend the duality to the limit as the bran...
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作者：Barbour, A. D.; Luczak, M. J.; Xia, A.
作者单位：University of Zurich; University of London; Queen Mary University London; University of Melbourne
摘要：For integer valued random variables, the translated Poisson distributions form a flexible family for approximation in total variation, in much the same way that the normal family is used for approximation in Kolmogorov distance. Using the Stein-Chen method, approximation can often be achieved with error bounds of the same order as those for the CLT. In this paper, an analogous theory, again based on Stein's method, is developed in the multivariate context. The approximating family consists of ...
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作者：Neuman, Eyal
作者单位：Imperial College London
摘要：We study the solutions of the stochastic heat equation driven by spatially inhomogeneous multiplicative white noise based on a fractal measure. We prove pathwise uniqueness for solutions of this equation when the noise co-efficient is Holder continuous of index gamma > 1 - eta/2(eta+1). Here eta is an element of (0, 1) is a constant that defines the spatial regularity of the noise.
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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：Duits, Maurice
作者单位：Royal Institute of Technology
摘要：We study the global fluctuations for a class of determinantal point processes coming from large systems of non-colliding processes and non-intersecting paths. Our main assumption is that the point processes are constructed by biorthogonal families that satisfy finite term recurrence relations. The central observation of the paper is that the fluctuations of multi-time or multi-layer linear statistics can be efficiently expressed in terms of the associated recurrence matrices. As a consequence,...
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作者：Banerjee, Sayan; Gordina, Maria; Mariano, Phanuel
作者单位：University of North Carolina; University of North Carolina Chapel Hill; University of Connecticut
摘要：We construct a non-Markovian coupling for hypoelliptic diffusions which are Brownian motions in the three-dimensional Heisenberg group. We then derive properties of this coupling such as estimates on the coupling rate, and upper and lower bounds on the total variation distance between the laws of the Brownian motions. Finally, we use these properties to prove gradient estimates for harmonic functions for the hypoelliptic Laplacian which is the generator of Brownian motion in the Heisenberg gro...
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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：Bordenave, Charles; Lelarge, Marc; Massoulie, Laurent
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Inria; Universite PSL; Ecole Normale Superieure (ENS); Institut Polytechnique de Paris; Ecole Polytechnique; Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Inria
摘要：A nonbacktracking walk on a graph is a directed path such that no edge is the inverse of its preceding edge. The nonbacktracking matrix of a graph is indexed by its directed edges and can be used to count nonbacktracking walks of a given length. It has been used recently in the context of community detection and has appeared previously in connection with the Ihara zeta function and in some generalizations of Ramanujan graphs. In this work, we study the largest eigenvalues of the nonbacktrackin...
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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.
