72 citations · 168 across the 4 of their papers we have counts for
5 papers
Recurrence of edge-reinforced random walk on a two-dimensional graph
Franz Merkl, Silke W. W. Rolles
We consider a linearly edge-reinforced random walk on a class of two-dimensional graphs with constant initial weights. The graphs are obtained from by replacing ever…
Linearly edge-reinforced random walks
Franz Merkl, Silke W. W. Rolles
We review results on linearly edge-reinforced random walks. On finite graphs, the process has the same distribution as a mixture of reversible Markov chains. This has applications…
Bayesian analysis for reversible Markov chains
Persi Diaconis, Silke W. W. Rolles
We introduce a natural conjugate prior for the transition matrix of a reversible Markov chain. This allows estimation and testing. The prior arises from random walk with reinforcem…
Asymptotic behavior of edge-reinforced random walks
Franz Merkl, Silke W. W. Rolles
In this article, we study linearly edge-reinforced random walk on general multi-level ladders for large initial edge weights. For infinite ladders, we show that the process can be…
Edge-reinforced random walk on a ladder
Franz Merkl, Silke W. W. Rolles
We prove that the edge-reinforced random walk on the ladder with initial weights is recurrent. The proof uses a known representation of the edge…