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We study a model of $n$ non-intersecting squared Bessel processes in theconfluent case: all paths start at time $t = 0$ at the same positive value $x =a$, remain positive, and are conditioned to end at time $t = T$ at $x = 0$. Inthe limit $n \to \infty$, after appropriate rescaling, the paths fill out aregion in the $tx$-plane that we describe explicitly. In particular, the pathsinitially stay away from the hard edge at $x = 0$, but at a certain criticaltime $t^*$ the smallest paths hit the hard edge and from then on are stuck toit. For $t \neq t^*$ we obtain the usual scaling limits from random matrixtheory, namely the sine, Airy, and Bessel kernels. A key fact is that thepositions of the paths at any time $t$ constitute a multiple orthogonalpolynomial ensemble, corresponding to a system of two modified Bessel-typeweights. As a consequence, there is a $3 \times 3$ matrix valuedRiemann-Hilbert problem characterizing this model, that we analyze in the large$n$ limit using the Deift-Zhou steepest descent method. There are some novelingredients in the Riemann-Hilbert analysis that are of independent interest.

Non-intersecting squared Bessel paths and multiple orthogonal polynomials for modified Bessel weights