Basdevant, Anne-Laure; Singh, Arvind Rate of growth of a transient cookie random walk. (English) Zbl 1191.60107 Electron. J. Probab. 13, 811-851 (2008). Summary: We consider a one-dimensional transient cookie random walk. It is known from a previous paper [A.-L. Basdevant and A. Singh, Probab. Theory Relat. Fields 141, No. 3–4, 625–645 (2008; Zbl 1141.60383)] that a cookie random walk \((X_n)\) has positive or zero speed according to some positive parameter \(\alpha >1\) or \(\leq 1\). In this article, we give the exact rate of growth of \(X_n\) in the zero speed regime, namely: for \(0<\alpha <1, X_{n}/n^{(\alpha +1)/2}\) converges in law to a Mittag-Leffler distribution whereas for \(\alpha =1, X_n(\log n)/n\) converges in probability to some positive constant. Cited in 2 ReviewsCited in 13 Documents MSC: 60K35 Interacting random processes; statistical mechanics type models; percolation theory 60J80 Branching processes (Galton-Watson, birth-and-death, etc.) 60F05 Central limit and other weak theorems Keywords:rates of transience; cookie or multi-excited random walk; branching process with migration PDF BibTeX XML Cite \textit{A.-L. Basdevant} and \textit{A. Singh}, Electron. J. Probab. 13, 811--851 (2008; Zbl 1191.60107) Full Text: DOI EMIS EuDML