Random walks in quenched i.i.d. space-time random environment are always a.s. diffusive

Abstract

We consider a general model of discrete-time random walk X-t on the lattice (nu), nu = 1,..., in a random environment xi={xi(t,x):(t,x)is an element of(nu+1)} with i.i.d. components xi(t,x). Previous results on the a.s. validity of the Central Limit Theorem for the quenched model required a small stochasticity condition. In this paper we show that the result holds provided only that an obvious non-degeneracy condition is met. The proof is based on the analysis of a suitable generating function, which allows to estimate L-2 norms by contour integrals

Invariance principle for the random conductance model

“…However, quenched invariance principles have been proven for several other discrete-time random walks in a dynamic random environment. In [BMP1] a QFCLT is obtained for random walks in space-time product environments by using Fourier-analytic methods. This result has been improved in [BMP2] to environments satisfying an exponential spatial mixing assumption and in [BZ] to Markovian environments by using more probabilistic techniques.…”

Асимптотика собственных значений дискретного оператора Шрeдингера с контактным потенциалом

“…Отметим, что аналогичное разложение при фиксированном k ∈ T d получено в [4], [5], [18] для определителей Фредгольма ∆ µ (k, z), ассоциированных с более общими операторами типа H µ (k).…”

О Спектральных Свойствах Обобщенной Модели Фридрихса

“…Далее, можно показать (для случая анали-тических функций v и D см. работу [18]; случай гладких функций требует некоторой модификации), что…”