Journal of Approximation Theory vol:162 issue:11 pages:2048-2077
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 infinity 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.