相关论文: Explicit contraction rates for a class of degenera…

This note studies Arveson's curvature invariant for d-contractions specialized to the case d=1 of a single contraction operator on a Hilbert space. It establishes a formula which gives an easy-to-understand meaning for the curvature of a…

We consider diffusion processes in Hilbert spaces with constant non-degenerate diffusion operators and show that, under broad assumptions on the drift, the transition probabilities of the process are positive on ellipsoids associated with…

In this work, we consider a class of hyperscaling violating Lifshitz-like black branes with metric scaling components $z=2$ and $\theta=-1$ whose corresponding holographic model can be treated as a non-relativistic fluid exhibiting…

Consider the differential operator H = -(1/m(x))L, where L is the N-dimensional Laplacian, in the weighted Hilbert space of square integrable functions on N-dimensional Euclidean space with weight m(x)dx. Here m(x) is a positive step…

Let $\alpha\in(0,2)$ and $d\in{\mathbb N}$. Consider the following SDE in ${\mathbb R}^d$:$${\rm d}X_t=b(t,X_t){\rm d} t+a(t,X_{t-}){\rm d} L^{(\alpha)}_t,\ \ X_0=x,$$where $L^{(\alpha)}$ is a $d$-dimensional rotationally invariant…

We study the Gibbs statistics of high-density hard-core configurations on a unit square lattice $\mathbb{Z}^2$, for a general Euclidean exclusion distance $D$. As a by-product, we solve the disk-packing problem on $\mathbb{Z}^2$ for disks…

We study the homogenization of first-order Hamilton-Jacobi equations on an infinite-dimensional Hilbert space, motivated by systems of infinitely many indistinguishable particles on the torus. A central difficulty is that the analysis takes…

The interpretation of water line emission from existing observations and future HIFI/Herschel data requires a detailed knowledge of collisional rate coefficients. Among all relevant collisional mechanisms, the rotational (de)excitation of…

We consider a degenerate infinite dimensional stochastic Hamiltonian system with multiplicative noise and establish the essential m-dissipativity on $L^2(\mu^{\Phi})$ of the corresponding Kolmogorov (backwards) operator. Here, $\Phi$ is the…

In this paper, we study the hypocoercivity for a class of linear kinetic equations with both transport and degenerately dissipative terms. As concrete examples, the relaxation operator, Fokker-Planck operator and linearized Boltzmann…

We are interested in the kernel of one-dimensional diffusion equations with continuous coefficients as evaluated by means of explicit discretization schemes of uniform step $h>0$ in the limit as $h\to0$. We consider both semidiscrete…

We classify integrable Hamiltonian equations in 3D with the Hamiltonian operator d/dx, where the Hamiltonian density h(u, w) is a function of two variables: dependent variable u and the non-locality w such that w_x=u_y. Based on the method…

We establish an equivalence between the rigidity of Wasserstein contraction along heat flows and the rigidity of Bakry--\'Emery gradient estimates for Lipschitz functions. Applying results of Ambrosio--Bru\'e--Semola and Han, we show that…

We consider a class of degenerate equations satisfying a parabolic H\"ormander condition, with coefficients that are measurable in time and H\"older continuous in the space variables. By utilizing a generalized notion of strong solution, we…

We study approximations of reflected It\^o diffusions on convex subsets $D$ of $\Rd$ by solutions of stochastic differential equations with penalization terms. We assume that the diffusion coefficients are merely measurable (possibly…

For a Banach space $B$ and for a class $\A$ of its bounded closed retracts, endowed with the Hausdorff metric, we prove that retractions on elements $A \in \A$ can be chosen to depend continuously on $A$, whenever nonconvexity of each $A…

We revisit the damped wave equation on two-dimensional torus where the damped region does not satisfy the geometric control condition. We show that if the damping vanishes as a H\"older function $|x|^{\beta}$, and in addition, the boundary…

We analyze degenerate, second-order, elliptic operators $H$ in divergence form on $L_2({\bf R}^{n}\times{\bf R}^{m})$. We assume the coefficients are real symmetric and $a_1H_\delta\geq H\geq a_2H_\delta$ for some $a_1,a_2>0$ where \[…

Building on advanced results on permutations, we show that it is possible to construct, for each irreducible representation of SU(N), an orthonormal basis labelled by the set of {\it standard Young tableaux} in which the matrix of the…

We perform a rigorous study of the Gibbs statistics of high-density hard-core random configurations on a unit triangular lattice $\mathbb{A}_2$ and a unit honeycomb graph $\mathbb{H}_2$, for any value of the (Euclidean) repulsion diameter…