Related papers: Polarity of points for Gaussian random fields
Random fields in nature often have, to a good approximation, Gaussian characteristics. We present the mathematical framework for a new and simple method for investigating the non-Gaussian contributions, based on counting the maxima and…
We study deviation probabilities for the number of high positioned particles in branching Brownian motion, and confirm a conjecture of Derrida and Shi (2016). We also solve the corresponding problem for the two-dimensional discrete Gaussian…
We prove that under fairly general conditions properly rescaled determinantal random point field converges to a generalized Gaussian random process.
We consider parabolic PDEs with randomly switching boundary conditions. In order to analyze these random PDEs, we consider more general stochastic hybrid systems and prove convergence to, and properties of, a stationary distribution.…
We investigate the quality of space approximation of a class of stochastic integral equations of convolution type with Gaussian noise. Such equations arise, for example, when considering mild solutions of stochastic fractional order partial…
We consider the limit behavior of partition function of directed polymers in random environment represented by linear model instead of a family of i.i.d.variables in $1+1$ dimensions. Under the assumption that the correlation decays…
In this article, we establish a probabilistic representation for the second-order moment of the solution of stochastic heat equation in $[0,1] \times \bR^d$, with multiplicative noise, which is fractional in time and colored in space. This…
In this paper, we establish lower and upper Gaussian bounds for the probability density of the mild solution to the stochastic heat equation with multiplicative noise and in any space dimension. The driving perturbation is a Gaussian noise…
Polarization of light signifies transversal, anisotropic and asymmetrical statistical property of electromagnetic radiation about direction of propagation. Traditionally, optical-polarization is characterized by Stokes theory susceptible to…
In this paper, we study the stochastic heat equation with a general multiplicative Gaussian noise that is white in time and colored in space. Both regularity and strict positivity of the densities of the solution have been established. The…
We consider a system of d non-linear stochastic heat equations in spatial dimension 1 driven by d-dimensional space-time white noise. The non-linearities appear both as additive drift terms and as multipliers of the noise. Using techniques…
We establish a probabilistic representation for a wide class of linear deterministic p.d.e.s with potential term, including the wave equation in spatial dimensions 1 to 3. Our representation applies to the heat equation, where it is related…
This work is concerned with a simple model for a polar fluid, a Gaussian field model based on the excess density and on the polarization. It is a convenient framework to implement the dielectric properties of correlated liquids that stem…
We consider the numerical approximation of Gaussian random fields on closed surfaces defined as the solution to a fractional stochastic partial differential equation (SPDE) with additive white noise. The SPDE involves two parameters…
We consider the polarization of thermal emission in the near-field of various materials including dielectrics and metallic systems with resonant surface modes. We find that at thermal equilibrium, the degree of polarization exhibits spatial…
This paper investigates an inverse potential problem for the stochastic heat equation driven by space-time Gaussian noise, which is spatially colored and temporally white. The objective is to determine the covariance operator of the random…
Random fields in nature often have, to a good approximation, Gaussian characteristics. For such fields, the relative densities of umbilical points -- topological defects which can be classified into three types -- have certain fixed values.…
Polar duality is a well-known concept from convex geometry and analysis. In the present paper, we study two symplectically covariant versions of polar duality keeping in mind their applications to quantum mechanics. The first variant makes…
We solve the infinite-dimensional stochastic differential equations (ISDEs) describing an infinite number of Brownian particles in $ \mathbb{R}^+$ interacting through the two-dimensional Coulomb potential. The equilibrium states of the…
Numerical methods for stochastic partial differential equations typically estimate moments of the solution from sampled paths. Instead, we shall directly target the deterministic equations satisfied by the first and second moments, as well…