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Correlated Random Walks on the Lattice: First-Passage Problems on Square, Hexagonal and Honeycomb Lattices with Boundaries

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SSDW05 - Modelling and Applications of Anomalous Diffusions

We present a general theory for determining the first-passage time distribution for random walks with one-step memory, the so-called Correlated or Persistent Random Walk. The first-passage theory relies on the knowledge of the occupation probability of the walk and we present cases on the square, honeycomb and hexagonal lattices where the occupation probability is known with different boundary conditions. We discuss how these boundary conditions affect the first-passage distribution and in certain cases give rise to bi- and multi-modal first-passage distributions. We conclude with some new results on how the persistent random walk on the Honeycomb lattice may be applied as a model to study the foraging behaviour of a colony of ants.  The work is done in collaboration with Luca Giuggioli. 

This talk is part of the Isaac Newton Institute Seminar Series series.

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