Two-Dimensional Moran Model: Final Altitude and Number of Resets

In this paper, we consider a two-dimension symmetric random walk with reset. We give, in the first part, some results about the distribution of every component. In the second part, we give some results about the final altitude Zn. Finally, we analyse the statistical properties of NnX, the number of resets (the number of returns to state 1 after n steps) of the first component of the random walk. As a principal tool in these studies, we use the probability generating function.

Automated summary

This paper focuses on a two-dimensional symmetric random walk with reset. The first part provides the distribution results of each component. The second part presents some results regarding the final altitude Zn. Finally, using the probability generating function, the statistical properties of NnX, the number of resets of the first component returning to state 1 after n steps in the random walk, are analyzed.