相关论文: Wick polynomials and time-evolution of cumulants

It has been known for a while that a nonlinear equation driven by singular noise must be interpreted in the re-normalized, or Wick, form. For the stochastic Burgers equation, Wick nonlinearity forces the solution to be a generalized process…

We derive an asymptotic expansion for the distribution of a compound sum of independent random variables, all having the same light-tailed subexponential distribution. The examples of a Poisson and geometric number of summands serve as an…

We summarize some of the recent developments which link certain problems in combinatorial theory related to random growth to random matrix theory.

We study the decomposition of free random variables in terms of their orthogonal replicas from a new perspective. First, we show that the mixed moments of orthogonal replicas with respect to the normalized linear functional $\Phi$ are…

Mathematical structure of the reflection coefficients for the one-dimensional Fokker-Planck equation is studied. A new formalism using differential operators is introduced and applied to the analysis in high- and low-energy regions.…

Numerical simulation of stochastic differential equations over long time intervals poses significant computational challenges. In this paper, we propose a novel recursive polynomial chaos evolution method that achieves model reduction…

The method of potential solutions of Fokker-Planck equations is used to develop a transport equation for the joint probability of N coupled stochastic variables with the Dirichlet distribution as its asymptotic solution. To ensure a bounded…

The method of self-consistent expansions is a powerful tool for handling strong coupling problems that might otherwise be beyond the reach of perturbation theory, providing surprisingly accurate approximations even at low order. First…

We establish closed-form expansions for the universal edge elimination polynomial of paths and cycles and their generating functions. This includes closed-form expansions for the bivariate matching polynomial, the bivariate chromatic…

We consider symplectic time integrators in numerical General Relativity and discuss both free and constrained evolution schemes. For free evolution of ADM-like equations we propose the use of the Stoermer-Verlet method, a standard…

Classical molecular dynamics simulation is performed mostly using the established velocity Verlet integrator or other symplectic propagation schemes. In this work, an alternative formulation of numerical propagators for classical molecular…

Colored knot polynomials possess a peculiar Z-expansion in certain combinations of differentials, which depends on the representation. The coefficients of this expansion are functions of the three variables (A,q,t) and can be considered as…

In this article we study exponential dichotomies for noninvertible linear difference equations in finite dimensions. After giving the definition, we study the extent to which the projection $P(k)$ in a dichotomy is unique. For equations on…

We obtain quenched hitting distributions to be compound Poissonian for a certain class of random dynamical systems. The theory is general and designed to accommodate non-uniformly expanding behavior and targets that do not overlap much with…

Probabilistic integration of a continuous dynamical system is a way of systematically introducing model error, at scales no larger than errors introduced by standard numerical discretisation, in order to enable thorough exploration of…

The dynamics of quantum systems can be approximated by the time propagation of Gaussian wave packets. Applying a time dependent variational principle, the time evolution of the parameters of the coupled Gaussian wave packets can be…

We derive a non-asymptotic expression for the moments of traces of monomials in several independent complex Wishart matrices, extending some explicit formulas available in the literature. We then deduce the explicit expression for the…

The Fokker-Planck equation is a partial differential equation that describes the evolution of a probability distribution over time. It is used to model a wide range of physical and biological phenomena, such as diffusion, chemical…

Combinatorial formulas expressing cyclic rook polynomials and cyclic permanents of rectangular matrices in terms of expansions along rows are presented

We establish sharp large deviation principles for cumulative rewards associated with a discrete-time renewal model, supposing that each renewal involves a broad-sense reward taking values in a real separable Banach space. The framework we…