Positively and negatively excited random walks on integers, with branching processes

By Elena Kosygina, M. Zerner. 2008

59 citations recorded by the source corpus.

We consider excited random walks on the integers with a bounded number of i.i.d. cookies per site which may induce drifts both to the left and to the right. We extend the criteria for recurrence and transience by M. Zerner and for positivity of speed by A.-L. Basdevant and A. Singh to this case and also prove an annealed central limit theorem. The proofs are based on results from the literature concerning branching processes with migration and make use of a certain renewal structure.

Subfields: Mathematical Physics, Molecular Biology, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/09931ee4b5e13f02745b718123c2bc40da096788

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mathematical Physics

1. Mikhail Menshikov
2. M. Vachkovskaia
3. Alejandro F. Ram'irez
4. Serguei Popov

In Molecular Biology

1. Mikhail Menshikov
2. M. Vachkovskaia
3. Alejandro F. Ram'irez
4. Serguei Popov

In Statistics and Probability

1. Mikhail Menshikov
2. M. Vachkovskaia
3. Alejandro F. Ram'irez
4. Serguei Popov

Citations in the corpus

• On a general many-dimensional excited random walk (2010, background): “Several papers have been written where the transient and ballisticity properties of this model are studied in random and deterministic environments, mainly in dimension d = 1 (see for example [9, 8, 2]).”