相关论文: Spectral Gap for the Stochastic Exchange Model

The spectral statistics of the circular billiard with a point-scatterer is investigated. In the semiclassical limit, the spectrum is demonstrated to be composed of two uncorrelated level sequences. The first corresponds to states for which…

The exact computation of the nearest-neighbor spacing distribution P(s) is performed for a rectangular billiard with point-like scatterer inside for periodic and Dirichlet boundary conditions and it is demonstrated that for large s this…

We introduce and study several random combinatorial billiard trajectories. Such a system, which depends on a fixed parameter $p\in(0,1)$, models a beam of light that travels in a Euclidean space, occasionally randomly reflecting off of a…

Polygonal billiards exhibit a rich and complex dynamical behavior. In recent years polygonal billiards have attracted great attention due to their application in the understanding of anomalous transport, but also at the fundamental level,…

In this paper we show a characterization of the joint spectral radius of a set of matrices as the limit of the $p$-radius of an associated probability distribution when $p$ tends to $\infty$. Allowing the set to have infinitely many…

In this article, we provide representations of European and American exchange option prices under stochastic volatility jump-diffusion (SVJD) dynamics following models by Merton (1976), Heston (1993), and Bates (1996). A Radon-Nikodym…

We prove that the stochastic Burgers equation, which is related to the Kardar-Parisi-Zhang/KPZ equation via weak derivative, is a "critical" scaling limit for density fluctuations for a family of non-integrable and non-stationary…

We consider the one-dimensional partially asymmetric exclusion model with open boundaries. The model describes a system of hard-core particles that hop stochastically in both directions with different rates. At both boundaries particles are…

We prove sharp spectral gap estimates on compact manifolds with integral curvature bounds. We generalize the results of Kr\"oger (Kr\"oger '92) as well as of Bakry and Qian (Bakry-Qian '00) to the case of integral curvature and confirm the…

We study the problem of detecting the presence of a single unknown spike in a rectangular data matrix, in a high-dimensional regime where the spike has fixed strength and the aspect ratio of the matrix converges to a finite limit. This…

Recently, Benzoni--Gavage, Danchin, Descombes, and Jamet have given a sufficient condition for linear and nonlinear stability of solitary wave solutions of Korteweg's model for phase-transitional isentropic gas dynamics in terms of…

We study the relation between escape rates and pressure in general dynamical systems with holes, where pressure is defined to be the difference between entropy and the sum of positive Lyapunov exponents. Central to the discussion is the…

We study the problem of option replication under constant proportional transaction costs in models where stochastic volatility and jumps are combined to capture the market's important features. Assuming some mild condition on the jump size…

The spectral excess theorem states that, in a regular graph G, the average excess, which is the mean of the numbers of vertices at maximum distance from a vertex, is bounded above by the spectral excess (a number that is computed by using…

We discuss the propagation of kinetic energy through billiard balls fixed in place along a one-dimensional segment. The number of billiard balls is assumed to be large but finite and we assume kinetic energy propagates following the usual…

In this paper we perform a numerical study of the spectra, eigenstates, and Lyapunov exponents of the skew-shift counterpart to Harper's equation. This study is motivated by various conjectures on the spectral theory of these…

Fang-Wu\cite{FW17} presented a explicit spectral gap for the O-U process on path space over a Riemannian manifold without boundary under the bounded Ricci curvature conditions. In this paper, we will extend these results to the case of the…

A well-known boundary observability inequality for the elasticity system establishes that the energy of the system can be estimated from the solution on a sufficiently large part of the boundary for a sufficiently large time. This…

We study a nonlinear recombination model from population genetics as a combinatorial version of the Kac-Boltzmann equation from kinetic theory. Following Kac's approach, the nonlinear model is approximated by a mean field linear evolution…

This paper is devoted to a high-dimensional mixed leadership stochastic differential game on a finite horizon in feedback information mode, where the control variables enter into the diffusion term of state equation. A verification theorem…