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Gillis' Random Walks on Graphs
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We consider a random walker on ad-regular graph. Starting from a fixed vertex, the first step is a unit step in any one of theddirections, with common probability 1/dfor each one. At any later step, the random walker moves in any one of the directions, with probabilityqfor a reversal of direction and probabilitypfor any other direction. This model was introduced and first studied by Gillis (1955), in the case when the graph is ad-dimensional square lattice. We prove that the Gillis random walk on ad-regular graph is recurrent if and only if the simple random walk on the graph is recurrent. The Green function of the Gillis random walk will be also given, in terms of that of the simple random walk.
Title: Gillis' Random Walks on Graphs
Description:
We consider a random walker on ad-regular graph.
Starting from a fixed vertex, the first step is a unit step in any one of theddirections, with common probability 1/dfor each one.
At any later step, the random walker moves in any one of the directions, with probabilityqfor a reversal of direction and probabilitypfor any other direction.
This model was introduced and first studied by Gillis (1955), in the case when the graph is ad-dimensional square lattice.
We prove that the Gillis random walk on ad-regular graph is recurrent if and only if the simple random walk on the graph is recurrent.
The Green function of the Gillis random walk will be also given, in terms of that of the simple random walk.
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