Mathematics – Classical Analysis and ODEs
Scientific paper
2009-11-19
Mathematics
Classical Analysis and ODEs
28 pages, 10 figures
Scientific paper
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.
Kuijlaars Arno B. J.
Roman Pablo
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