Recurrence and transience for non‐Archimedean and directed graphs
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DOI: 10.1002/mana.70040
Abstract: We introduce notions of recurrence and transience for graphs over a non‐Archimedean ordered field. To achieve this, we establish a connection between these graphs and random walks on directed graphs over the reals. In particular,… read more here.
Keywords: directed graphs; non archimedean; recurrence transience; transience non ... See more keywords
Markov chains with heavy-tailed increments and asymptotically zero drift
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DOI: 10.1214/19-ejp322
Abstract: We study the recurrence/transience phase transition for Markov chains on $\mathbb{R}_+$, $\mathbb{R}$, and $\mathbb{R}^2$ whose increments have heavy tails with exponent in $(1,2)$ and asymptotically zero mean. This is the infinite-variance analogue of the classical… read more here.
Keywords: markov chains; asymptotically zero; drift; recurrence transience ... See more keywords