相关论文: $t^{1/3}$ Superdiffusivity of Finite-Range Asymmet…
This paper provides a new tauberian approach to the study of quantitative time asymptotics of collisionless transport semigroups with general diffuse boundary operators. We obtain an (almost) optimal algebraic rate of convergence to…
The one-dimensional triplet contact process with diffusion (TCPD) model has been studied using fast multispin GPU Monte Carlo simulations. In particular, the particle density \rho and the density of pairs of neighboring particles \rho_p…
Let $M$ be a $d$-dimensional connected compact Riemannian manifold with boundary $\partial M$, let $V\in C^2(M)$ such that $\mu({\rm d} x):={\rm e}^{V(x)}{\rm d} x$ is a probability measure, and let $X_t$ be the diffusion process generated…
A discrete-time totally asymmetric simple exclusion process on a lattice with open boundaries is considered. There are particles of different types. The type of a particle is characterized by the probability that a particle moves to a…
We revisit, both numerically and analytically, the finite-time blowup of the infinite-energy solution of 3D Euler equations of stagnation-point-type introduced by Gibbon et al. (1999). By employing the method of mapping to regular systems,…
We obtain the large deviation functional of a density profile for the asymmetric exclusion process of L sites with open boundary conditions when the asymmetry scales like 1/L. We recover as limiting cases the expressions derived recently…
For the speed-change exclusion process on $\mathbb{Z}^d$ reversible with respect to the product Bernoulli measure, we prove that its semigroup $P_t$ satisfies a variance decay $\operatorname{Var}[P_t u] = C_u t^{-\frac{d}{2}} +…
We consider an infinite dimensional diffusion on $T^{\mathbb Z^d}$, where $T$ is the circle, defined by an infinitesimal generator of the form $L=\sum_{i\in\mathbb Z^d}\left(\frac{a_i(\eta)}{2}\partial^2_i +b_i(\eta)\partial_i\right)$, with…
E. B. Davies et B. Simon have shown (among other things) the following result: if T is an n\times n matrix such that its spectrum \sigma(T) is included in the open unit disc \mathbb{D}=\{z\in\mathbb{C}:\,|z|<1\} and if…
In this paper we solve a selection problem for multidimensional SDE $d X^\varepsilon(t)=a(X^\varepsilon(t)) d t+\varepsilon \sigma(X^\varepsilon(t))\, d W(t)$, where the drift and diffusion are locally Lipschitz continuous outside of a…
We develop a higher-order asymptotic analysis for the semi-hard triplet loss using the Edgeworth expansion. It is known that this loss function enforces that embeddings of similar samples are close while those of dissimilar samples are…
We study the properties of points in $[0,1]^d$ generated by applying Hilbert's space-filling curve to uniformly distributed points in $[0,1]$. For deterministic sampling we obtain a discrepancy of $O(n^{-1/d})$ for $d\ge2$. For random…
By means of rather general arguments, based on an approach due to Derrida that makes use of samples of finite size, we analyse the effective diffusivity and drift tensors in certain types of random medium in which the motion of the…
We find explicit upper bounds for the density of marginals of continuous diffusions where we assume that the diffusion coefficient is constant and the drift is solely assumed to be progressively measurable and locally bounded. In one…
We give bounds for the total variation distance between the solutions to two stochastic differential equations starting at the same point and with close coefficients, which applies in particular to the distance between an exact solution and…
Using mode coupling theory and dynamical Monte-Carlo simulations we investigate the scaling behaviour of the dynamical structure function of a two-species asymmetric simple exclusion process, consisting of two coupled single-lane asymmetric…
For the case of approximation of convection--diffusion equations using piecewise affine continuous finite elements a new edge-based nonlinear diffusion operator is proposed that makes the scheme satisfy a discrete maximum principle. The…
Consider a superdiffusion $X$ on $\mathbb R^d$ corresponding to the semilinear operator $\mathcal{A}(u)=Lu+\beta u-ku^2,$ where $L$ is a second order elliptic operator, $\beta(\cdot)$ is in the Kato class and bounded from above, and…
We consider an exclusion process on a periodic one-dimensional lattice where all particles perform simple symmetric exclusion at rate $1$ except for a single tracer particle, which performs partially simple asymmetric exclusion with rate…
A homogenization problem of infinite dimensional diffusion processes indexed by ${\mathbf Z}^d$ having periodic drift coefficients is considered. By an application of the uniform ergodic theorem for infinite dimensional diffusion processes…