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Mathematical Physics, math-ph, Condensed Matter, Statistical Mechanics, cond-mat.stat-mech,Mathematics, Combinatorics, math.CO,Mathematics, Mathematical Physics, math.MP
Abstract:
A generalization of Tutte polynomial involved in the evaluation of the
moments of the integrated geometric Brownian in the Ito formalism is discussed.
The new combinatorial invariant depends on the order in which the sequence of
contraction-deletions have been performed on the graph. Thus, this work
provides a motivation for studying an order-dependent Tutte polynomial in the
context of stochastic differential equations. We show that in the limit of the
control parameters encoding the ordering going to zero, the multivariate
Tutte-Fortuin-Kasteleyn polynomial is recovered.
