Аннотация:
In the last decades, some remarkable advances were achieved
in the asymptotic of the so-called random matching problem.
We focus on the case of continuous-time Markov processes,
and discuss in particular the asymptotic of the transport
distance between the occupation measure of a Brownian motion
on a flat torus, and the Lebesgue measure. The result is
established thanks to a comparison with an auxiliary random
measure, called the random interlacement, for which the
transport distance naturally features subadditivity.
Possible generalizations and their connection with some conjectures
that appeared in the physical literature will be further discussed, as
time allows. Joint work with D.Trevisan.
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