Gambler's ruin, preferential attachment, and branching random walk: New results for classical problems using direct and indirect couplings

We first discuss the duration of gambler's ruin, one of the oldest problems in probability theory, and use direct coupling to show it stochastically increases when games are made fairer. We then use indirect coupling to quantify node degree joint distributional approximations for preferential attachment random graphs by nonhomogeneous Poisson process spacings. Finally, we quantify exponential approximations for the footprint of critical branching random walk using indirect coupling. We also discuss connections with machine learning, statistics, health care management, and Stein's method.

This talk contains results from work with Tobias Johnson, Rhonda Righter, Adrian Rollin, Nathan Ross, and Sheldon Ross.

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