论文标题
超临界零范围过程不变的度量的凝结
Condensation of the invariant measures of the supercritical zero range processes
论文作者
论文摘要
对于$α\ geq 1 $，让$ g：\ mathbb n \ to \ mathbb r _+$由$ g（0）= 0 $，$ g（1）= 1 $，$ g（k）=（k/k-1）^α$，$ k \ geq 2 $。考虑离散的圆环$ \ mathbb t_l $的对称最近的邻居零范围过程，其中粒子从$ k $粒子占用的站点跳跃到具有$ g（k）$的邻居之一。 Armendáriz和loulakis \ cite {al09}证明了合奏的等效形式，用于以$ a> 2 $ $α> 2 $的超临界零范围过程的不变度度量。我们将它们的结果推广到所有$α\ geq 1 $。
For $α\geq 1$, let $g:\mathbb N\to\mathbb R_+$ be given by $g(0)=0$, $g(1)=1$, $g(k)=(k/k-1)^α$, $k\geq 2$. Consider the symmetric nearest neighbour zero range process on the discrete torus $\mathbb T_L$ in which a particle jumps from a site, occupied by $k$ particles, to one of its neighbors with rate $g(k)$. Armendáriz and Loulakis\cite{al09} proved a strong form of the equivalence of ensembles for the invariant measure of the supercritical zero range process with $α>2$. We generalize their result to all $α\geq 1$.
