Dear Colleagues,
We would like to invite you to the following
SPASS seminar, jointly organized by UniPi, SNS, UniFi and UniSi:
Annealed quantitative estimates for the 2D-discrete random matching problemby
Francesco Mattesini (MPI Leipzig)
The seminar will take place on
TUE, 30.05.2023 at
14:00 CET in Aula Seminari, Department of Mathematics, University of Pisa and streamed online
here.
The organizers,
A. Agazzi, G. Bet, A. Caraceni, F. Grotto, G. Zanco
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Abstract: The
optimal matching problem is a classical random variational problem
which may be interpreted as an optimal transport problem between two
random discrete measures. Its easier instance deals with matching 2 n-clouds of i. i. d. uniformly distributed points. In recent years
Caracciolo-Lucibello-Parisi-Sicuro made exact predictions on the
convergence of the rescaled cost thanks to a first order linearization
of the Monge-Amp\'ere equation. This approach was later justified by
Ambrosio-Stra-Trevisan and quantitative bounds for the convergence of
the proxies were later shown by Ambrosio-Glaudo-Trevisan. Such
techniques have been repurposed by Benedetto-Caglioti to study the case of i. i. d. random points with non-constant densities. By
subadditivity and PDE arguments Ambrosio-Goldman-Trevisan were able to
justify the latter for the convergence of the rescaled cost. We show
annealed quantitative upper bounds for the approximating transport map
in the case of i. i. d. points and weakly correlated points with
non-constant densities. We extend our results to the case of unbalanced
matching, i. e. matching between point clouds of different size and to
point clouds sampled from a positive recurrent Markov chain.
Joint work with N. Clozeau (IST Austria).