相关论文: On the two-point function of the one-dimensional K…
By using Malliavin calculus, explicit derivative formulae are established for a class of semi-linear functional stochastic partial differential equations with additive or multiplicative noise. As applications, gradient estimates and Harnack…
We study the overlap distribution of two particles chosen under the Gibbs measure at two temperatures for the branching Brownian motion. We first prove the convergence of the overlap distribution using the extended convergence of the…
We consider weakly-coupled QFT in AdS at finite temperature. We compute the holographic thermal two-point function of scalar operators in the boundary theory. We present analytic expressions for leading corrections due to local quartic…
The partition function of the directed polymer model on Z^{2+1} undergoes a phase transition in a suitable continuum and weak disorder limit. In this paper, we focus on a window around the critical point. Exploiting local renewal theorems,…
The stochastic rotational invariance of an integration by parts formula inspired by the Bismut approach to Malliavin calculus is proved in the framework of the Lie symmetry theory of stochastic differential equations. The non-trivial effect…
The logarithm of the diagonal matrix element of a high power of a random matrix converges to the Cole-Hopf solution of the Kardar-Parisi-Zhang equation in the sense of one-point distributions.
An explicit Fredholm determinant formula is derived for the multipoint distribution of the height function of the totally asymmetric simple exclusion process (TASEP) with arbitrary right-finite initial condition. The method is by solving…
A polymer model given in terms of beads, interacting through Hookean springs and hydrodynamic forces, is studied. Brownian dynamics description of this bead-spring polymer model is extended to multiple resolutions. Using this multiscale…
We study the fixed-time spatial covariance of the KPZ equation with flat initial profile. Using Malliavin calculus and a Clark-Ocone representation, we show that as $|x|\to\infty$, $\mathrm{Cov}[h(t,x),h(t,0)]$ is governed by a…
Motivated by the recent advances in the theory of stochastic partial differential equations involving nonlinear functions of distributions, like the Kardar-Parisi-Zhang (KPZ) equation, we reconsider the unique solvability of one-dimensional…
We calculate the probability distribution function (PDF) of an overdamped Brownian particle moving in a periodic potential energy landscape $U(x)$. The PDF is found by solving the corresponding Smoluchowski diffusion equation. We derive the…
We study a planar two-temperature diffusion of a Brownian particle in a parabolic potential. The diffusion process is defined in terms of two Langevin equations with two different effective temperatures in the X and the Y directions. In the…
We apply the Dirichlet forms version of Malliavin calculus to stochastic differential equations with jumps. As in the continuous case this weakens significantly the assumptions on the coefficients of the SDE. In spite of the use of the…
A novel refinement of the conventional treatment of Kadanoff--Baym equations is suggested. Besides the Boltzmann equation another differential equation is used for calculating the evolution of the non-equilibrium two-point function.…
In this paper we introduce a Hilbert space-valued Malliavin calculus for Poisson random measures. It is solely based on elementary principles from the theory of point processes and basic moment estimates, and thus allows for a simple…
We analyze the equations governing the evolution of distributions of the work and the heat exchanged with the environment by a manipulated stochastic system, by means of a compact and general derivation. We obtain explicit solutions for…
We consider the Rosenzweig-Porter model of random matrix which interpolates between Poisson and gaussian unitary statistics and compute exactly the two-point correlation function. Asymptotic formulas for this function are given near the…
Various solutions to the discrete Schwarzian KdV equation are discussed. We first derive the bilinear difference equations of Hirota type of the discrete Schwarzian KP equation, which is decomposed into three discrete two-dimensional Toda…
Consider stochastic functional differential equations, whose coefficients depend on past histories. The solution determines a non-Markov process. In the present paper, we shall obtain the existence of smooth densities for joint…
We consider the dispersion-generalized KP-II equation on a partially periodic domain in the weakly dispersive regime. We use Fourier decoupling techniques to derive essentially sharp Strichartz estimates. With these at hand, we show global…