2 research outputs found
Random walks in Euclidean space
Consider a sequence of independent random isometries of Euclidean space with
a previously fixed probability law. Apply these isometries successively to the
origin and consider the sequence of random points that we obtain this way. We
prove a local limit theorem under a suitable moment condition and a necessary
non-degeneracy condition. Under stronger hypothesis, we prove a limit theorem
on a wide range of scales: between e^(-cl^(1/4)) and l^(1/2), where l is the
number of steps.Comment: 62 pages, 1 figure, revision based on referee's report, proofs and
results unchange