Some Classes Of Distributions On The Non-Negative Lattice

迭代图系统（II）：伯努利渗流与层级晶格上的临界指数普适类

Iterated Graph Systems (II): Bernoulli percolation and critical-exponent universality classes on hierarchical lattices

研究层级晶格上的伯努利渗流，证明有限维数族不能决定普适类，并否证普适性需可公度重整化尺度的猜想。

Moment growth bounds on continuous time Markov processes on non-negative integer lattices

We consider Markov processes in continuous time with state space $\posint^N$ and provide two sufficient conditions and one necessary condition for the existence of moments $E(\|X(t)\|^r)$ of all orders $r \in \nat$ for all $t \geq 0$. The sufficient conditions also guarantee an exponential in time growth bound for the moments. The class of processes studied have finitely many state independent jumpsize vectors $ν_1,\dots,ν_M$. This class of processes arise naturally in many applications such as stochastic models of chemical kinetics, population dynamics and queueing theory for example. We also…