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Out-of-equilibrium random walks

Part of: Limit theorems Markov processes

Published online by Cambridge University Press:  24 September 2020

Leonardo A. Videla
Leonardo A. Videla*
Affiliation:
Universidad de Valparaíso
*
*Postal address: Instituto de Ingeniería Matemática - CIMFAV, General Cruz 222, 5th floor, Valparaíso, Chile. Email: leonardo.videla@postgrado.uv.cl
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Abstract

We study the long-term behaviour of a random walker embedded in a growing sequence of graphs. We define a (generally non-Markovian) real-valued stochastic process, called the knowledge process, that represents the ratio between the number of vertices already visited by the walker and the current size of the graph. We mainly focus on the case where the underlying graph sequence is the growing sequence of complete graphs.

Keywords

Random walksgrowing graphsasymptotics

MSC classification

Primary: 60J28: Applications of continuous-time Markov processes on discrete state spaces
Secondary: 60F15: Strong theorems 60F25: $L^p$-limit theorems
Type
Original Article
Information
Advances in Applied Probability , Volume 52 , Issue 3 , September 2020 , pp. 772 - 797
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Copyright
© Applied Probability Trust 2020

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