可数状态均场相互作用粒子系统不变测度的准势作为率函数的充分条件
A sufficient condition for the quasipotential to be the rate function of the invariant measure of countable-state mean-field interacting particle systems
AI总结：
本文研究了可数状态均场相互作用粒子系统中，准势作为率函数的充分条件，并通过反例说明在稳态下准势可能并非率函数。
摘要：
本文考虑了马尔可夫均场相互作用粒子系统在可数无限状态空间上的不变测度族，并研究其大偏差渐进行为。Freidlin-Wentzell准势通常是用于序列为粒子数索引的不变测度序列的率函数候选者。本文提供了两个反例，其中准势并非率函数。准势源于有限时间 horizon 的考虑。然而，某些障碍在任何有限时间 horizon 内难以克服，但在稳态情况下可以跨越。因此，准势在某些点上为无穷大，而率函数在这些点上为有限值。在突出这一现象后，本文研究了一些相互作用粒子系统类别的充分条件，使得可以继续断言Freidlin-Wentzell准势确实是率函数。
英文摘要：
This paper considers the family of invariant measures of Markovian mean-field interacting particle systems on a countably infinite state space and studies its large deviation asymptotics. The Freidlin-Wentzell quasipotential is the usual candidate rate function for the sequence of invariant measures indexed by the number of particles. The paper provides two counterexamples where the quasipotential is not the rate function. The quasipotential arises from finite horizon considerations. However there are certain barriers that cannot be surmounted easily in any finite time horizon, but these barriers can be crossed in the stationary regime. Consequently, the quasipotential is infinite at some points where the rate function is finite. After highlighting this phenomenon, the paper studies some sufficient conditions on a class of interacting particle systems under which one can continue to assert that the Freidlin-Wentzell quasipotential is indeed the rate function.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
