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作者：Borga, Jacopo; Slivken, Erik
作者单位：University of Zurich; Universite PSL; Universite Paris-Dauphine
摘要：We describe the limit (for two topologies) of large uniform random square permutations, that is, permutations where every point is a record. The starting point for all our results is a sampling procedure for asymptotically uniform square permutations. Building on that, we first describe the global behavior by showing that these permutations have a permuton limit which can be described by a random rectangle. We also explore fluctuations about this random rectangle, which we can describe through...
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作者：Ahlberg, Daniel; Deijfen, Maria; Hoffman, Christopher
作者单位：Stockholm University; University of Washington; University of Washington Seattle
摘要：The two-type Richardson model describes the growth of two competing infection types on the two or higher dimensional integer lattice. For types that spread with the same intensity, it is known that there is a positive probability for infinite coexistence, while for types with different intensities, it is conjectured that infinite coexistence is not possible. In this paper we study the two-type Richardson model in the upper half-plane Z x Z(+), and prove that coexistence of two types starting o...
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作者：Han, Ruijian; Ye, Rougang; Tan, Chunxi; Chen, Kani
作者单位：Hong Kong University of Science & Technology
摘要：The Bradley-Terry model is a fundamental model in the analysis of network data involving paired comparison. Assuming every pair of subjects in the network have an equal number of comparisons, Simons and Yao (Ann. Statist. 27 (1999) 1041-1060) established an asymptotic theory for statistical estimation in the Bradley-Terry model. In practice, when the size of the network becomes large, the paired comparisons are generally sparse. The sparsity can be characterized by the probability p(n) that a ...
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作者：Allan, Andrew L.; Cohen, Samuel N.
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Oxford
摘要：We study the problem of pathwise stochastic optimal control, where the optimization is performed for each fixed realisation of the driving noise, by phrasing the problem in terms of the optimal control of rough differential equations. We investigate the degeneracy phenomenon induced by directly controlling the coefficient of the noise term, and propose a simple procedure to resolve this degeneracy whilst retaining dynamic programming As an application, we use pathwise stochastic control in the...
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作者：Banerjee, Sayan; Budhiraja, Amarjit
作者单位：University of North Carolina; University of North Carolina Chapel Hill
摘要：We obtain rates of convergence to stationarity in L-1-Wasserstein distance for a d-dimensional reflected Brownian motion (RBM) in the nonnegative orthant that are explicit in the dimension and the system parameters. The results are then applied to a class of RBMs considered in (Blanchet and Xinyun (2016)) and to rank-based diffusions including the Atlas model. In both cases, we obtain explicit rates and bounds on relaxation times. In the first case we improve the relaxation time estimates of O...
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作者：Hutzenthaler, Martin; Pieper, Daniel
作者单位：University of Duisburg Essen
摘要：Propagation of chaos is a well-studied phenomenon and shows that weakly interacting diffusions may become independent as the system size converges to infinity. Most of the literature focuses on the case of exchangeable systems where all involved diffusions have the same distribution and are of the same size. In this paper, we analyze the case where only a few diffusions start outside of an accessible trap. Our main result shows that in this sparse regime the system of weakly interacting diffus...
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作者：Cohen-Alloro, Omri; Peled, Ron
作者单位：Tel Aviv University
摘要：Motivated by questions on the delocalization of random surfaces, we prove that random surfaces satisfying a Lipschitz constraint rarely develop extremal gradients. Previous proofs of this fact relied on reflection positivity and were thus limited to random surfaces defined on highly symmetric graphs, whereas our argument applies to general graphs. Our proof makes use of a cluster algorithm and reflection transformation for random surfaces of the type introduced by Swendsen-Wang, Wolff and Ever...
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作者：Poisat, Julien; Simenhaus, Francois
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite PSL; Universite Paris-Dauphine
摘要：We consider a one-dimensional simple random walk surviving among a field of static soft obstacles: each time it meets an obstacle the walk is killed with probability 1 - e(-beta), where beta is a positive and fixed parameter. The positions of the obstacles are sampled independently from the walk and according to a renewal process. The increments between consecutive obstacles, or gaps, are assumed to have a power-law decaying tail with exponent gamma > 0. We prove convergence in law for the pro...
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作者：Dean, Justin; Ganesh, Ayalvadi; Crane, Edward
作者单位：University of Bristol
摘要：We consider an infinite-server queue into which customers arrive according to a Cox process and have independent service times with a general distribution. We prove a functional large deviations principle for the equilibrium queue length process. The model is motivated by a linear feed-forward gene regulatory network, in which the rate of protein synthesis is modulated by the number of RNA molecules present in a cell. The system can be modelled as a nonstandard tandem of infinite-server queues...
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作者：Durmus, Alain; Guillin, Arnaud; Monmarche, Pierre
作者单位：Universite Paris Saclay; Universite Clermont Auvergne (UCA); Sorbonne Universite; Universite Paris Cite
摘要：The Bouncy Particle Sampler (BPS) is a Monte Carlo Markov chain algorithm to sample from a target density known up to a multiplicative constant. This method is based on a kinetic piecewise deterministic Markov process for which the target measure is invariant. This paper deals with theoretical properties of BPS. First, we establish geometric ergodicity of the associated semi-group under weaker conditions than in (Ann. Statist. 47 (2019) 1268-1287) both on the target distribution and the veloci...
