2 research outputs found
Probability recurrences on simple graphs in a forest building process
Consider the following process on a simple graph with no isolated vertices: Randomly order the edges and remove an edge if and only if the edge is incident to two vertices already incident to some preceding edge. This process results in a spanning forest of the graph.
Recurrences are given for the process for multiple families of graphs, and the probability of obtaining components in the above process is given by a new method for the Fan graph . An approach to proving a previously published conjecture is also discussed
Enumerative Theory for the Tsetlin Library
The Tsetlin library is a well-studied Markov chain on the symmetric group
. It has stationary distribution the Luce model, a
nonuniform distribution on , which appears in psychology, horse race
betting, and tournament poker. Simple enumerative questions, such as ``what is
the distribution of the top cards?'' or ``what is the distribution of the
bottom cards?'' are long open. We settle these questions and draw attention
to a host of parallel questions on the extension to the chambers of a
hyperplane arrangement.Comment: 23 pages, 1 figur