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- Title
Speed of Excited Random Walks with Long Backward Steps.
- Authors
Nguyen, Tuan-Minh
- Abstract
We study a model of multi-excited random walk with non-nearest neighbour steps on Z , in which the walk can jump from a vertex x to either x + 1 or x - i with i ∈ { 1 , 2 , ⋯ , L } , L ≥ 1 . We first point out the multi-type branching structure of this random walk and then prove a limit theorem for a related multi-type Galton–Watson process with emigration, which is of independent interest. Combining this result and the method introduced by Basdevant and Singh (Probab Theory Relat Fields 141:3–4, 2008), we extend their result (w.r.t. the case L = 1 ) to our model. More specifically, we show that in the regime of transience to the right, the walk has positive speed if and only if the expected total drift δ > 2 . This confirms a special case of a conjecture proposed by Davis and Peterson.
- Publication
Journal of Statistical Physics, 2022, Vol 188, Issue 1, p1
- ISSN
0022-4715
- Publication type
Article
- DOI
10.1007/s10955-022-02926-2