Título: First hitting distribution in different regimes: a probabilistic proof of Cooper&Frieze's First Visit Time Lemma
Palestrante: Elisabetta Scoppola (Università Roma Tre)
Data: 27/09/2021
Horário: 15:00hrs às 16:00hrs
Local: Transmissão online
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Resumo: I present results recently obtained with Francesco Manzo e Matteo Quattropani. We present an alternative proof of the so-called First Visit Time Lemma (FVTL), originally presented by Cooper and Frieze. We work in the original setting, considering a growing sequence of irreducible Markov chains on n states. We assume that the chain is rapidly mixing and with a stationary measure with no entry being either too small nor too large. Under these assumptions, the FVTL shows the exponential decay of the distribution of the hitting time of a given state x, for the chain started at stationarity, up to a small multiplicative correction. While the proof by Cooper and Frieze is based on tools from complex analysis, and it requires an additional assumption on a generating function, we present a completely probabilistic proof, relying on the theory of quasi-stationary distributions and on strong-stationary times arguments. In addition, under the same set of assumptions, we provide some quantitative control on the Doob's transform of the chain on the complement of the state x. I will also discuss the relation of this result with general results, previously obtained, providing an exact formula for the first hitting distribution via conditional strong quasi-stationary times.
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