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作者：Gu, Chenlin
作者单位：Universite PSL; Ecole Normale Superieure (ENS)
摘要：We present an efficient algorithm to solve elliptic Dirichlet problems defined on the cluster of supercritical Z(d)-Bernoulli percolation, as a generalization of the iterative method proposed by S. Armstrong, A. Hannukainen, T. Kuusi and J.-C. Mourrat (ESAIM Math. Model. Numer. Anal. (2021) 55 37-55). We also explore the two-scale expansion on the infinite cluster of percolation, and use it to give a rigorous analysis of the algorithm.
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作者：Collevecchio, Andrea; Tuan-Minh Nguyen; Volkov, Stanislav
作者单位：Monash University; Lund University
摘要：We consider a nonlinear vertex-reinforced jump process (VRJP(w)) on Z with an increasing measurable weight function w : [1, infinity) -> [1, infinity) and initial weights equal to one. Our main goal is to study the asymptotic behaviour of VRJP(w) depending on the integrability of the reciprocal of w. In particular, we prove that if integral(infinity)(1) du/w(u) = infinity then the process is recurrent, that is, it visits each vertex infinitely often and all local times are unbounded. On the ot...
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作者：Hartarsky, Ivailo; Martinelli, Fabio; Toninelli, Cristina
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite PSL; Universite Paris-Dauphine; Roma Tre University
摘要：Motivated by kinetically constrained interacting particle systems (KCM), we consider a reversible coalescing and branching simple exclusion process on a general finite graph G = (V, E) dual to the biased voter model on G. Our main goal is tight bounds on its logarithmic Sobolev constant and relaxation time, with particular focus on the delicate slightly supercritical regime in which the equilibrium density of particles tends to zero as vertical bar V vertical bar -> infinity. Our results allow...
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作者：Pain, Michel; Senizergues, Delphin
作者单位：New York University; University of British Columbia
摘要：Weighted recursive trees are built by adding successively vertices with predetermined weights to a tree: each new vertex is attached to a parent chosen randomly proportionally to its weight. Under some assumptions on the sequence of weights, the first order for the height of such trees has been recently established by one of the authors. In this paper, we obtain the second and third orders in the asymptotic expansion of the height of weighted recursive trees, under similar assumptions. Our met...
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作者：Bartl, Daniel; Mendelson, Shahar
作者单位：University of Vienna; Australian National University
摘要：We develop a novel procedure for estimating the optimizer of general convex stochastic optimization problems of the form min(x is an element of chi) E[F (x, xi)] when the given data is a finite independent sample selected according to xi. The procedure is based on a median-of-means tournament, and is the first procedure that exhibits the optimal statistical performance in heavy tailed situations: we recover the asymptotic rates dictated by the central limit theorem in a nonasymptotic manner on...
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作者：Flandoli, Franco; Hofmanova, Martina; Luo, Dejun; Nilssen, Torstein
作者单位：Scuola Normale Superiore di Pisa; University of Bielefeld; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; University of Agder
摘要：We are concerned with the problem of global well-posedness of the 3D Navier-Stokes equations on the torus with unitary viscosity. While a full answer to this question seems to be out of reach of the current techniques, we establish a regularization by a deterministic vector field. More precisely, we consider the vorticity form of the system perturbed by an additional transport type term. Such a perturbation conserves the enstrophy and therefore a priori it does not imply any smoothing. Our mai...
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作者：Holden, Nina; Lyons, Russell
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; Indiana University System; Indiana University Bloomington
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作者：Fountoulakis, Nikolaos; Iyer, Tejas; Mailler, Cecile; Sulzbach, Henning
作者单位：University of Birmingham; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; University of Bath
摘要：We study a general model of random dynamical simplicial complexes and derive a formula for the asymptotic degree distribution. This asymptotic formula generalises results for a number of existing models, including random Apollonian networks and the weighted random recursive tree. It also confirms results on the scale-free nature of complex quantum network manifolds in dimensions d > 2, and special types of network geometry with Flavour models studied in the physics literature by Bianconi and R...
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作者：Bo, Lijun; Liao, Huafu; Yu, Xiang
作者单位：Xidian University; National University of Singapore; Hong Kong Polytechnic University
摘要：This paper investigates the finite horizon risk-sensitive portfolio optimization in a regime-switching credit market with physical and information-induced default contagion. It is assumed that the underlying regime-switching process has countable states and is unobservable. The stochastic control problem is formulated under partial observations of asset prices and sequential default events. By establishing a martingale representation theorem based on incomplete and phasing out filtration, we c...
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作者：Broutin, Nicolas; Duquesne, Thomas; Wang, Minmin
作者单位：Universite Paris Cite; Sorbonne Universite; University of Sussex
摘要：Motivated by limits of critical inhomogeneous random graphs, we construct a family of measured metric spaces that we call continuous multiplicative graphs, that are expected to be the universal limit of graphs related to the multiplicative coalescent (the Erdos-Renyi random graph, more generally the so-called rank-one inhomogeneous random graphs of various types, and the configuration model). At the discrete level, the construction relies on a new point of view on (discrete) inhomogeneous rand...
