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Spectral Duality and Reset-Neutral Distributions in Random Walks with Multi-Site Geometric Resetting
We study the gambler's ruin problem for a biased random walk on $\{0,1,\dots,a\}$ under multi-site geometric resetting: at each step the walker is reset with probability $γ\in(0,1)$ to a position drawn from a distribution $π$ over $m$ interior sites. Using renewal theory, we derive a closed-form exp
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