Recurrence relations and vector equilibrium problems arising from a model of non-intersecting squared Bessel paths

  • Authors:

  • A. B. J. Kuijlaars;P. Román

  • Affiliations:

  • Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200b - bus 2400, 3001 Leuven, Belgium;Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200b - bus 2400, 3001 Leuven, Belgium and CIEM, FaMAF, Universidad Nacional de Córdoba, Medina Allende s/n Ciudad Un ...

  • Venue:
  • Journal of Approximation Theory
  • Year:
  • 2010

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Abstract

In this paper we consider the model of n non-intersecting squared Bessel processes with parameter @a, 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-~ 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 @a, 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.