Individual behaviors of oriented walks

[摘要] Given an infinite sequence t = (epsilon (k))(k) of -1 and +1, we consider the oriented walk defined by S-n(t) = Sigma (n)(k=1) epsilon (1)epsilon (2)...epsilon (k). The set of t's whose behaviors satisfy S-n(t) similar to bn(tau) is considered (b epsilon R and 0 < less than or equal to 1 being fixed) and its Hausdorff dimension is calculated. A two-dimensional model is also studied. A three-dimensional model is described, but the problem remains open. (C) 2000 Elsevier Science B.V. All rights reserved. MSG: 28A78; 42A55; 60G50.

[发布日期] 2000-12-01

[关键词] oriented walk;random walk;Hausdorff dimension;Riesz product