Spanning tree invariants, loop systems and doubly stochastic matrices

✍ Scribed by Ricardo Gómez; José Miguel Salazar

• Publisher: Elsevier Science
• Year: 2010
• Tongue: English
• Weight: 260 KB
• Volume: 432
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/j.laa.2009.09.002

✦ Synopsis

The spanning tree invariant of Lind and Tuncel [12] is observed in the context of loop systems of Markov chains. For n = 1, 2, 3 the spanning tree invariants of the loop systems of a Markov chain determined by an irreducible stochastic (n × n)-matrix P coincide if and only if P is doubly stochastic and, in this case, the common value of the spanning tree invariants of the loop systems is n.