CIEM   05476
CENTRO DE INVESTIGACION Y ESTUDIOS DE MATEMATICA
Unidad Ejecutora - UE
artículos
Título:
Recurrence relations and vector equilibrium problems arising from a model of non-intersecting squared Bessel paths
Autor/es:
A. KUIJLAARS; P. ROMÁN
Revista:
Enviado a publicar
Editorial:
Enviado a publicar
Referencias:
Año: 2009 p. 1 - 28
Resumen:
In this paper we consider the model of $n$ non-intersecting squared Bessel
processes with parameter $\alpha$, in the confluent case where all particles
start, at time $t=0$, at the same positive value $x=a$, remain positive, and
end, at time $T=t$, at the position $x=0$. The positions of the paths have a
limiting mean density as $n\to\infty$ which is characterized by a vector
equilibrium problem. We show how to obtain this equilibrium problem from
different considerations involving the recurrence relations for multiple
orthogonal polynomials associated with the modified Bessel functions.
We also extend the situation by rescaling the parameter $\alpha$, letting it
increase proportionally to $n$ as $n$ increases. In this case we also analyze
the recurrence relation and obtain a vector equilibrium problem for it.