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The Matsumoto and Yor process and infinite dimensional hyperbolic space
The Matsumoto\,--Yor process is , where
is a Brownian motion. It is shown that it is the limit of the radial
part of the Brownian motion at the bottom of the spectrum on the hyperbolic
space of dimension , when tends to infinity. Analogous processes on
infinite series of non compact symmetric spaces and on regular trees are
described.Comment: 3
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