"Infinite Systems of
Non-Colliding Generalized Meanders and Riemann-Liouville Differintegrals",
Yor's generalized meander is a
temporally inhomogeneous modification of
the $2(\nu+1)$-dimensional Bessel process with $\nu > -1$,
in which the inhomogeneity is indexed by
$\kappa \in [0, 2(\nu+1))$.
We introduce the non-colliding particle systems
of the generalized meanders and prove that
they are Pfaffian processes, in the sense
that any multitime correlation function is
given by a Pfaffian.
In the infinite particle limit,
we show that the elements of matrix kernels
of the obtained infinite Pfaffian processes
are generally expressed by
the Riemann-Liouville differintegrals
of functions comprising the Bessel functions $J_{\nu}$
used in the fractional calculus,
where orders of differintegration
are determined by $\nu-\kappa$.
As special cases of the two parameters
$(\nu, \kappa)$,
the present infinite systems include
the quaternion determinantal processes
studied by Forrester, Nagao and Honner
and by Nagao, which exhibit
the temporal transitions
between the universality classes of
random matrix theory.
