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math.PR2019★ 1 cited
The Directed Edge Reinforced Random Walk: The Ant Mill Phenomenon
Dirk Erhard, Tertuliano Franco, Guilherme Reis
We define here a \textit{directed edge reinforced random walk} on a connected locally finite graph. As the name suggests, this walk keeps track of its past, and gives a bias toward…
math.PR2019
The Slow Bond Random Walk and the Snapping Out Brownian Motion
Dirk Erhard, Tertuliano Franco, Diogo S. da Silva
We consider the continuous time symmetric random walk with a slow bond on , which rates are equal to for all bonds, except for the bond of vertices , whi…