# Znanstveni kolokvij SMDa: prof. Ilya Molchanov

lokacija:
PMF Split
vrijeme:
13.09.2019 - 12:00 - 13:00
U sklopu redovnog kolokvija Znanstvenog razreda Splitskog matematičkog društva

prof. Ilya Molchanov
Institute of Mathematical Statistics and Actuarial Science, University of Bern

će održati predavanje pod naslovom:

The semigroup of metric measure spaces and its infinitely divisible probability measures

Predavanje će se održati u petak 13.9. u 12:00u dvorani B3-17 Odjela za matematiku PMF-a, Ruđera Boškovića 33.
Pozivamo sve zainteresirane da prisustvuju predavanju.

Sažetak:

The semigroup of metric measure spaces and its infinitely divisible probability measures
(joint work with Steve Evans, Berkeley)

A metric measure space (also called Gromov triple) is a complete, separable metric space equipped with a probability measure that has full support. Two such spaces are equivalent if they are isometric as metric spaces via an isometry that maps the probability measure on the first space to the probability measure on the second. We consider the natural binary operation on this space that takes two metric measure spaces and forms their Cartesian product equipped with the sum of the two metrics and the product of the two probability measures. We show that the metric measure spaces equipped with this operation form a cancellative, commutative, Polish semigroup with a translation invariant metric. There is an explicit family of continuous semicharacters that is extremely useful for establishing that there are no infinitely divisible elements and that each element has a unique factorization into prime elements.

We investigate the interaction between the semigroup structure and the natural action of the positive real numbers on this space that arises from scaling the metric. We establish that there is no analogue of the law of large numbers and characterize the infinitely divisible probability measures and the L\’evy processes on this semigroup, characterize the stable probability measures and establish a counterpart of the LePage representation for the latter class.