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作者：Owada, Takashi
作者单位：Purdue University System; Purdue University
摘要：We investigate the topological dynamics of extreme sample clouds generated by a heavy tail distribution on R-d by establishing various limit theorems for Betti numbers, a basic quantifier of algebraic topology. It then turns out that the growth rate of the Betti numbers and the properties of the limiting processes all depend on the distance of the region of interest from the weak core, that is, the area in which random points are placed sufficiently densely to connect with one another. If the ...
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作者：Pichler, Georg; Piantanida, Pablo; Matz, Gerald
作者单位：Technische Universitat Wien; Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS)
摘要：Let (X, Y) denote n independent, identically distributed copies of two arbitrarily correlated Rademacher random variables (X, Y). We prove that the inequality I( f (X); g (Y)) <= I(X; Y) holds for any two Boolean functions: f, g: {-1,1}(n) -> {-1,1} [I(.;.) denotes mutual information]. We further show that equality in general is achieved only by the dictator functions f(x) = +/- g(x) = +/- x(i), i is an element of {1,2,...,n}.
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作者：Loeper, Gregoire
作者单位：Monash University; Monash University
摘要：We consider a model of linear market impact, and address the problem of replicating a contingent claim in this framework. We derive a nonlinear Black-Scholes equation that provides an exact replication strategy. This equation is fully nonlinear and singular, but we show that it is well posed, and we prove existence of smooth solutions for a large class of final payoffs, both for constant and local volatility. To obtain regularity of the solutions, we develop an original method based on Legendr...
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作者：Bolley, Francois; Chafai, Djalil; Fontbona, Joaquin
作者单位：Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite; Universite Paris Cite; Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universidad de Chile
摘要：We study the long-time behavior of the dynamics of interacting planar Brownian particles, confined by an external field and subject to a singular pair repulsion. The invariant law is an exchangeable Boltzmann-Gibbs measure. For a special inverse temperature, it matches the Coulomb gas known as the complex Ginibre ensemble. The difficulty comes from the interaction which is not convex, in contrast with the case of one-dimensional log-gases associated with the Dyson Brownian motion. Despite the ...
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作者：Sasada, Makiko
作者单位：University of Tokyo
摘要：In the diffusive hydrodynamic limit for a symmetric interacting particle system (such as the exclusion process, the zero range process, the stochastic Ginzburg-Landau model, the energy exchange model), a possibly nonlinear diffusion equation is derived as the hydrodynamic equation. The bulk diffusion coefficient of the limiting equation is given by the Green-Kubo formula and it can be characterized by a variational formula. In the case the system satisfies the gradient condition, the variation...
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作者：Bally, Vlad; Goreac, Dan; Rabiet, Victor
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Gustave-Eiffel; Universite Gustave-Eiffel
摘要：We consider stochastic differential systems driven by a Brownian motion and a Poisson point measure where the intensity measure of jumps depends on the solution. This behavior is natural for several physical models (such as Boltzmann equation, piecewise deterministic Markov processes, etc.). First, we give sufficient conditions guaranteeing that the semigroup associated with such an equation preserves regularity by mapping the space of k-times differentiable bounded functions into itself. Furt...
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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：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：Cetin, Umut
作者单位：University of London; London School Economics & Political Science
摘要：We develop a new class of path transformations for one-dimensional diffusions that are tailored to alter their long-run behaviour from transient to recurrent or vice versa. This immediately leads to a formula for the distribution of the first exit times of diffusions, which is recently characterised by Karatzas and Ruf [Probab. Theory Related Fields 164 (2016) 1027-1069] as the minimal solution of an appropriate Cauchy problem under more stringent conditions. A particular limit of these transf...
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作者：Ma, Ruibo; Durrett, Rick
作者单位：Duke University
摘要：We study an evolutionary game in which a producer at x gives birth at rate 1 to an offspring sent to a randomly chosen point in x + N-c, while a cheater at x gives birth at rate lambda > 1 times the fraction of producers in x + N-d and sends its offspring to a randomly chosen point in x + N-c. We first study this game on the d-dimensional torus (Z mod L)(d) with N-d = (Z mod L)(d) and N-c = the 2d nearest neighbors. If we let L -> infinity then t -> infinity the fraction of producers converges...
