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作者：Turova, Tatyana S.
作者单位：Lund University
摘要：We consider the system of particles on a finite interval with pairwise nearest neighbours interaction and external force. This model was introduced by Malyshev [Probl. Inf. Transm. 51 (2015) 31-36] to study the flow of charged particles on a rigorous mathematical level. It is a simplified version of a 3-dimensional classical Coulomb gas model. We study Gibbs distribution at finite positive temperature extending recent results on the zero temperature case (ground states). We derive the asymptot...
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作者：Alt, Johannes; Erdos, Laszlo; Krueger, Torben
作者单位：Institute of Science & Technology - Austria
摘要：We consider large random matrices X with centered, independent entries, which have comparable but not necessarily identical variances. Girko's circular law asserts that the spectrum is supported in a disk and in case of identical variances, the limiting density is uniform. In this special case, the local circular law by Bourgade et al. [Probab. Theory Related Fields 159 (2014) 545-595; Probab. Theory Related Fields 159 (2014) 619-660] shows that the empirical density converges even locally on ...
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作者：De Angelis, Tiziano; Ferrari, Giorgio; Moriarty, John
作者单位：University of Leeds; University of Bielefeld; University of London; Queen Mary University London
摘要：This paper analyses two-player nonzero-sum games of optimal stopping on a class of linear regular diffusions with not nonsingular boundary behaviour [in the sense of Ito and McKean (Diffusion Processes and Their Sample Paths (1974) Springer, page 108)]. We provide sufficient conditions under which Nash equilibria are realised by each player stopping the diffusion at one of the two boundary points of an interval. The boundaries of this interval solve a system of algebraic equations. We also pro...
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作者：Dombry, Clement; Hashorva, Enkelejd; Soulier, Philippe
作者单位：Universite Marie et Louis Pasteur; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); University of Lausanne
摘要：The goal of this paper is an exhaustive investigation of the link between the tail measure of a regularly varying time series and its spectral tail process, independently introduced in [Owada and Samorodnitsky (2012)] and [Stochastic Process. Appl. 119 (2009) 1055-1080]. Our main result is to prove in an abstract framework that there is a one-to-one correspondence between these two objects, and given one of them to show that it is always possible to build a time series of which it will be the ...
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作者：Reygner, Julien
作者单位：Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees; Universite Gustave-Eiffel
摘要：We consider particle systems with mean-field interactions whose distribution is invariant by translations. Under the assumption that the system seen from its centre of mass be reversible with respect to a Gibbs measure, we establish large deviation principles for its empirical measure at equilibrium. Our study covers the cases of McKean-Vlasov particle systems without external potential, and systems of rank-based interacting diffusions. Depending on the strength of the interaction, the large d...
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作者：Lionnet, Arnaud; dos Reis, Goncalo; Szpruch, Lukasz
作者单位：Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees; University of Edinburgh
摘要：The theory of Forward-Backward Stochastic Differential Equations (FBSDEs) paves a way to probabilistic numerical methods for nonlinear parabolic PDEs. The majority of the results on the numerical methods for FBSDEs relies on the global Lipschitz assumption, which is not satisfied for a number of important cases such as the Fisher-KPP or the FitzHugh- Nagumo equations. Furthermore, it has been shown in [Ann. Appl. Probab. 25 (2015) 2563-2625] that for BSDEs with monotone drivers having polynomi...
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作者：Cuchiero, Christa; Larsson, Martin; Svaluto-Ferro, Sara
作者单位：University of Vienna; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：Polynomial jump-diffusions constitute a class of tractable stochastic models with wide applicability in areas such as mathematical finance and population genetics. We provide a full parameterization of polynomial jump-diffusions on the unit simplex under natural structural hypotheses on the jumps. As a stepping stone, we characterize well-posedness of the martingale problem for polynomial operators on general compact state spaces.
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作者：Jagannath, Aukosh; Ko, Justin; Sen, Subhabrata
作者单位：University of Toronto; Stanford University
摘要：We study the asymptotic behavior of the Max kappa-cut on a family of sparse, inhomogeneous random graphs. In the large degree limit, the leading term is a variational problem, involving the ground state of a constrained inhomogeneous Potts spin glass. We derive a Parisi-type formula for the free energy of this model, with possible constraints on the proportions, and derive the limiting ground state energy by a suitable zero temperature limit.
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作者：Touboul, Jonathan
作者单位：Institut National de la Sante et de la Recherche Medicale (Inserm); Universite PSL; College de France
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作者：Schumacher, Christoph; Schwarzenberger, Fabian; Veselic, Ivan
作者单位：Dortmund University of Technology
摘要：We consider random fields indexed by finite subsets of an amenable discrete group, taking values in the Banach-space of bounded right-continuous functions. The field is assumed to be equivariant, local, coordinate-wise monotone and almost additive, with finite range dependence. Using the theory of quasi-tilings we prove an uniform ergodic theorem, more precisely, that averages along a Folner sequence converge uniformly to a limiting function. Moreover, we give explicit error estimates for the ...
