The speed of frogs with drift on ℤ

2015/05/19 by Thomas Höfelsauer, Höfelsauer, Thomas, Felizitas Weidner +1 · 1 citation
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1505.05006

openalex publication_date 2015/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article we consider the frog model with drift on ℤ and investigate the behaviour of the cloud of the frogs. In particular, we show that the speed of the minimum equals the speed of a single frog and prove some properties of the speed of the maximum. In addition, we show a limit theorem for the empirical distribution.

Citations

• The shape theorem for the frog model with random initial configuration

Cited by

• A zero-one law for recurrence and transience of frog processes

Related

• On the range of the transient frog model on Z
• Critical drift estimates for the frog model on trees
• On the minimal drift for recurrence in the frog model on d-ary trees
• The frog model with drift on R
• Improved critical drift estimates for the frog model on trees