Year: 2006
Type: preprint
Abstract: This investigation is motivated by a result we proved recently for the random transposition random walk: the distance from the starting point of the walk has a phase transition from a linear regime to a sublinear regime at time $n/2$. Here, we study three new examples. It is trivial that the distance for random walk on the hypercube is smooth and is given by one simple formula. In the case of random adjacent transpositions, we find that there is no phase transition even though the distance has different scalings in three different regimes. In the case of a random 3-regular graph, there is a phase transition from linear growth to a constant equal to the diameter of the graph, at time $3\log_2 n$.
Source: arXiv (Cornell University)
Authors: Berestycki, Nathanael, Durrett, Rick
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2949844156