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2019 Slowdown for the geodesic-biased random walk
Mikhail Beliayeu, Petr Chmel, Bhargav Narayanan, Jan Petr
Electron. Commun. Probab. 24: 1-8 (2019). DOI: 10.1214/19-ECP276


Given a connected graph $G$ with some subset of its vertices excited and a fixed target vertex, in the geodesic-biased random walk on $G$, a random walker moves as follows: from an unexcited vertex, she moves to a uniformly random neighbour, whereas from an excited vertex, she takes one step along some fixed shortest path towards the target vertex. We show, perhaps counterintuitively, that the geodesic-bias can slow the random walker down exponentially: there exist connected, bounded-degree $n$-vertex graphs with excitations where the expected hitting time of a fixed target is at least $\exp (\sqrt [4]{n} / 100)$.


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Mikhail Beliayeu. Petr Chmel. Bhargav Narayanan. Jan Petr. "Slowdown for the geodesic-biased random walk." Electron. Commun. Probab. 24 1 - 8, 2019.


Received: 4 September 2019; Accepted: 7 November 2019; Published: 2019
First available in Project Euclid: 14 November 2019

zbMATH: 07142644
MathSciNet: MR4040940
Digital Object Identifier: 10.1214/19-ECP276

Primary: 60G50
Secondary: 60C05, 60J10


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