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作者：Sun, Wen
作者单位：Chinese Academy of Sciences; University of Science & Technology of China, CAS
摘要：A pathwise large deviation result is proved for the pure jump models of the k-nary interacting particle system introduced by Kolokoltsov (Markov Process. Related Fields 12 (2006) 95-138; Nonlinear Markov Processes and Kinetic Equations (2010) Cambridge Univ. Press) that generalize classical Boltzmann's collision model, Smoluchovski's coagulation model and many others. The upper bound is obtained by following the standard methods (KOV (Comm. Pure Appl. Math. 42 (1989) 115-137)) of using a proce...
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作者：Zhang, Xiaolong; Zhang, Xicheng
作者单位：Beijing Institute of Technology
摘要：In this paper we establish the optimal regularity estimates for the Cauchy problem of stochastic kinetic equations with random coefficients in anisotropic Besov spaces. As applications, we study the nonlinear filtering problem for a degenerate diffusion process, and obtain the existence and regularity of conditional probability densities under a few assumptions. Moreover, we also show the well-posedness for a class of super-linear growth stochastic kinetic equations driven by velocity-time whi...
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作者：Pymar, Richard; Rivera, Nicolas
作者单位：University of London; University of Greenwich; Universidad de Valparaiso
摘要：Given a transition matrix P indexed by a finite set V of vertices, the voter model is a discrete-time Markov chain in {0, 1}V where at each time-step a randomly chosen vertex x imitates the opinion of vertex y with probability P(x, y). The noisy voter model is a variation of the voter model in which vertices may change their opinions by the action of an external noise. The strength of this noise is measured by an extra parameter p is an element of [0, 1]. In this work we analyse the density pr...
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作者：Zhou, Jianjun
作者单位：Northwest A&F University - China
摘要：This paper introduces a notion of viscosity solutions for second order elated with infinite-horizon optimal control problems for stochastic differential equations with infinite delay. We identify the value functional of optimal control problems as unique viscosity solution to associated second order elliptic HJB equations with infinite delay. We also show that our notion of viscosity solutions is consistent with the corresponding notion of classical solutions, and satisfies a stability property.
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作者：Bungert, Leon; Calder, Jeff; Roith, Tim
作者单位：University of Wurzburg; University of Minnesota System; University of Minnesota Twin Cities; Helmholtz Association; Deutsches Elektronen-Synchrotron (DESY)
摘要：In this paper we prove the first quantitative convergence rates for the graph infinity Laplace equation for length scales at the connectivity threshold. In the graph-based semisupervised learning community this equation is also known as Lipschitz learning. The graph infinity Laplace equation is characterized by the metric on the underlying space, and convergence rates follow from convergence rates for graph distances. At the connectivity threshold, this problem is related to Euclidean first pa...
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作者：Lodewijks, Bas; Ortgiese, Marcel
作者单位：University of Augsburg; University of Bath
摘要：We study a generalisation of the random recursive tree (RRT) model and its multigraph counterpart, the uniform directed acyclic graph (DAG). Here, vertices are equipped with a random vertex-weight representing initial inhomogeneities in the network, so that a new vertex connects to one of the old vertices with a probability that is proportional to their vertex-weight. We first identify the asymptotic degree distribution of a uniformly chosen vertex for a general vertex-weight distribution. For...
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作者：Movassagh, Ramis; Szegedy, Mario; Wang, Guanyang
作者单位：Rutgers University System; Rutgers University New Brunswick; Rutgers University System; Rutgers University New Brunswick
摘要：Sourav Chatterjee, Persi Diaconis, Allan Sly, and Lingfu Zhang (Ann. Probab. 50 (2022) 1-17), prompted by a question of Ramis Movassagh, renewed the study of a process proposed in the early 1980s by Jean Bourgain. A state vector v is an element of R-n, labeled with the vertices of a connected graph, G, changes in discrete time steps following the simple rule that at each step a random edge (i, j) is picked and v(i) and v(j) are both replaced by their average (v(i) + v(j))/2. It is easy to see ...
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作者：Gundlach, Rowel; van der Hofstad, Remco
作者单位：Eindhoven University of Technology
摘要：We analyse the cluster discovered by invasion percolation on a branching process with a power-law offspring distribution. Invasion percolation is a paradigm model of self-organised criticality, where criticality is approach without tuning any parameter. By performing invasion percolation for n steps, and letting n -> infinity, we find an infinite subtree, called the invasion percolation cluster (IPC). A notable feature of the IPC is its geometry that consists of a unique path to infinity (also...
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作者：Izyurov, Konstantin; Kemppainen, Antti; Tuisku, Petri
作者单位：University of Helsinki
摘要：We compute rigorously the scaling limit of multipoint energy correlations in the critical Ising model on a torus. For the one -point function, averaged between horizontal and vertical edges of the square lattice, this result has been known since the 1969 work of Ferdinand and Fischer. We propose an alternative proof, in a slightly greater generality, via a new exact formula in terms of determinants of discrete Laplacians. We also compute the main term of the asymptotics of the difference E(EV ...
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作者：Atar, Rami; Castiel, Eyal; Reiman, Martin I.
作者单位：Technion Israel Institute of Technology; Columbia University
摘要：The standard setting for studying parallel server systems (PSS) at the diffusion scale is based on the heavy traffic condition (HTC), which assumes that the underlying static allocation linear program (LP) is critical and has a unique solution. This solution determines the graph of basic activities, which identifies the set of activities (i.e., class-server pairs) that are operational. In this paper we explore the extended HTC, where the LP is merely assumed to be critical. Because multiple so...
