相关论文: A de Bruijn identity for discrete random variables

We analyze the asymptotic behaviour of the heat kernel defined by a stochastically perturbed geodesic flow on the cotangent bundle of a Riemannian manifold for small time and small diffusion parameter. This extends WKB-type methods to a…

The heat kernel expansion is a very convenient tool for studying one-loop divergences, anomalies and various asymptotics of the effective action. The aim of this report is to collect useful information on the heat kernel coefficients…

This paper explores the properties of multipliers associated with discrete analogues of fractional integrals, revealing intriguing connections with Dirichlet characters, Euler's identity, and Dedekind zeta functions of quadratic imaginary…

We consider a natural generalisation of the Laplace type operators for the case of non-commutative (Moyal star) product. We demonstrate existence of a power law asymptotic expansion for the heat kernel of such operators on T^n. First four…

We prove an important property of the binomial transform: it converts multiplication by the discrete variable into a certain difference operator. We also consider the case of dividing by the discrete variable. The properties presented here…

We consider in this paper a perturbation of the standard semilinear heat equation by a term involving the space derivative and a non-local term. In some earlier work (Abdelhedi-Zaag JDE 2021), we constructed a blow-up solution for that…

We present a numerical method that consistently implements thermal fluctuations and hydrodynamic interactions to the motion of Brownian particles dispersed in incompressible host fluids. In this method, the thermal fluctuations are…

We present analytical methods to calculate the magnetic response of non-interacting electrons constrained to a domain with boundaries and submitted to a uniform magnetic field. Two different methods of calculation are considered - one…

We study discrete nonlinear parabolic stochastic heat equations of the form, $u_{n+1}(x)-u_n(x)=(\mathcal {L}u_n)(x)+\sigma(u_n(x))\xi_n(x)$, for $n\in {\mathbf{Z}}_+$ and $x\in {\mathbf{Z}}^d$, where $\boldsymbol \xi:=\{\xi_n(x)\}_{n\ge…

We consider a particular class of n-dimensional homogeneous diffusions all of which have an identity diffusion matrix and a drift function that is piecewise constant and scale invariant. Abstract stochastic calculus immediately gives us…

We give a purely combinatorial proof of the Glaisher-Crofton identity which derives from the analysis of discrete structures generated by iterated second derivative. The argument illustrates utility of symbolic and generating function…

A binary modified de Bruijn sequence is an infinite and periodic binary sequence derived by removing a zero from the longest run of zeros in a binary de Bruijn sequence. The minimal polynomial of the modified sequence is its unique…

We give a necessary and sufficient condition for the existence of a local solution of the inverse problem of calculus of variations in terms of the identical vanishing of the variation of a functional on an extended space (with the number…

In this short communication we present an original way to couple the Brownian motion and the heat equation. More in general, we suggest a way for coupling the Langevin equation for a particle, which describes a single realization of its…

Our earlier results on the temperature inversion properties and the ellipticisation of the finite temperature internal energy on odd spheres are extended to orbifold factors of odd spheres and then to other thermodynamic quantities, in…

We investigate a random integral which provides a natural example of an imaginary exponential functional of Brownian motion. This functional shows up in the study of the binary annihilation process, within the Doi-Peliti formalism for…

We prove the existence and uniqueness of a mild solution for a class of non-autonomous parabolic mixed stochastic partial differential equations defined on a bounded open subset $D \subset \mathbb{R}^d$ and involving standard and fractional…

The main aim of this paper is to provide a unified approach to deriving identities for the Bernstein polynomials using a novel generating function. We derive various functional equations and differential equations using this generating…

We prove a homogenization theorem for a class of quadratic convolution energies with random coefficients. Under suitably stated hypotheses of ergodicity and stationarity we prove that the $\Gamma$-limit of such energy is almost surely a…

In this paper, we develop variational integrators for the nonequilibrium thermodynamics of simple closed systems. These integrators are obtained by a discretization of the Lagrangian variational formulation of nonequilibrium thermodynamics…