A Functional Central Limit Theorem for Polaron Path Measures
نویسندگان
چکیده
The application of the Feynman-Kac formula to Polaron models quantum theory leads path measure Brownian motion perturbed by a pair potential that is translation invariant both in space and time. An important problem this context validity central limit theorem infinite volume. We show existence relevant volume limits functional generality includes Frohlich polaron for all coupling constants. proofs are based on an extension novel method Mukherjee Varadhan.
منابع مشابه
A Functional Central Limit Theorem for The
In this paper, we present a functional fluid limit theorem and a functional central limit theorem for a queue with an infinity of servers M/GI/∞. The system is represented by a point-measure valued process keeping track of the remaining processing times of the customers in service. The convergence in law of a sequence of such processes after rescaling is proved by compactness-uniqueness methods...
متن کاملA functional central limit theorem for PEPA
We present a functional central limit theorem which quantifies, as a stochastic process, the difference between a PEPA model’s underlying CTMC and its fluid approximation. We generalise existing theory to handle the case of non-smooth rate functions, which is an issue particular to modelling problems in computer science. We verify the weak convergence empirically and suggest future avenues for ...
متن کاملA functional combinatorial central limit theorem
The paper establishes a functional version of the Hoeffding combinatorial central limit theorem. First, a pre-limiting Gaussian process approximation is defined, and is shown to be at a distance of the order of the Lyapounov ratio from the original random process. Distance is measured by comparison of expectations of smooth functionals of the processes, and the argument is by way of Stein’s met...
متن کاملA functional central limit theorem for regenerative chains
Using the regenerative scheme of [8], we establish a functional central limit theorem (FCLT) for discrete time stochastic processes (chains) with summable memory decay. Furthermore, under stronger assumptions on the memory decay, we identify the limiting variance in terms of the process only. As applications, we define classes of binary autoregressive processes and power-law Ising chains for wh...
متن کاملThe Central Limit Theorem for uniformly strong mixing measures
The theorem of Shannon-McMillan-Breiman states that for every generating partition on an ergodic system, the exponential decay rate of the measure of cylinder sets equals the metric entropy almost everywhere (provided the entropy is finite). In this paper we prove that the measure of cylinder sets are lognormally distributed for strongly mixing systems and infinite partitions and show that the ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Communications on Pure and Applied Mathematics
سال: 2022
ISSN: ['1097-0312', '0010-3640']
DOI: https://doi.org/10.1002/cpa.22080