A quenched functional central limit theorem for planar random walks in random sceneries

作者：Guillotin Plantard Nadine^*; Poisat Julien; dos Santos Renato Soares

来源：Electronic Communications in Probability, 2014, 19(0): 1-9.

DOI：10.1214/ECP.v19-3002

• Random walk in random scenery
• Limit theorem
• Local time
• Associated Random Variables

Random walks in random sceneries (RWRS) are simple examples of stochastic processes in disordered media. They were introduced at the end of the 70's by Kesten-Spitzer and Borodin, motivated by the construction of new self-similar processes with stationary increments. Two sources of randomness enter in their definition: a random field xi = (xi(x))(x is an element of Zd) of i.i.d. random variables, which is called the random scenery, and a random walk S = (S-n)(n is an element of N) evolving in Z(d), independent of the scenery. The RWRS Z = (Z(n))(n is an element of N) is then defined as the accumulated scenery along the trajectory of the random walk, i.e., Z(n) := Sigma(n)(k=1) xi(S-k). The law of Z under the joint law of xi and S is called "annealed", and the conditional law given xi is called "quenched". Recently, functional central limit theorems under the quenched law were proved for Z by the first two authors for a class of transient random walks including walks with finite variance in dimension d >= 3. In this paper we extend their results to dimension d = 2

• 出版日期2014-1-28