# Excursion Processes Associated with Elliptic Combinatorics

@article{Baba2017ExcursionPA,
title={Excursion Processes Associated with Elliptic Combinatorics},
author={Hiroya Baba and Makoto Katori},
journal={Journal of Statistical Physics},
year={2017},
volume={171},
pages={1035-1066}
}
• Published 1 November 2017
• Mathematics
• Journal of Statistical Physics
Researching elliptic analogues for equalities and formulas is a new trend in enumerative combinatorics which has followed the previous trend of studying q-analogues. Recently Schlosser proposed a lattice path model in the square lattice with a family of totally elliptic weight-functions including several complex parameters and discussed an elliptic extension of the binomial theorem. In the present paper, we introduce a family of discrete-time excursion processes on $$\mathbb {Z}$$Z starting…

## References

SHOWING 1-10 OF 24 REFERENCES

We introduce seven families of stochastic systems of interacting particles in one-dimension corresponding to the seven families of irreducible reduced affine root systems. We prove that they are
The Bessel process with parameter $D>1$ and the Dyson model of interacting Brownian motions with coupling constant $\beta >0$ are extended to the processes in which the drift term and the interaction
A weight-dependent generalization of the binomial theorem for noncommuting variables is presented. This result extends the well-known binomial theorem for q-commuting variables by a generic weight
Description: A self–contained study of the various applications and developments of discrete distribution theory Written by a well–known researcher in the field, Discrete q–Distributions features an
We introduce an elliptic extension of Dyson’s Brownian motion model, which is a temporally inhomogeneous diffusion process of noncolliding particles defined on a circle. Using elliptic determinant
1 Bessel Process1.1 One-Dimensional BrownianMotion (BM) 1.2 Martingale Polynomials of BM 1.3 Drift Transform 1.4 Quadratic Variation 1.5 Stochastic Integration 1.6 Ito's Formula 1.7 Complex Brownian
• Mathematics
• 1996
I: Theory.- I. Stochastic processes in general.- II. Linear diffusions.- III. Stochastic calculus.- IV. Brownian motion.- V. Local time as a Markov process.- VI. Differential systems associated to