Optimal Transport and Uncertainty

Session

main contributions

26 Nov 2021, 14:30

Dipartimento di Matematica (Pisa)

1. Euclidean Random Assignment Problems, old and new

Prof. Matteo D'Achille (Université Paris-Est Créteil)

26/11/2021, 14:30

An Euclidean Random Assignment Problem (ERAP in short) is as follows:

• there are two $n$-sets $\mathcal{B}=(B_i)_{i=1}^n$ (blue points) and $\mathcal{R}=(R_i)_{I=1}^n$ (red points) of i.i.d. random variables valued on a metric space $(\Omega,D)$ according to a prob. measure $\nu$ (disorder);

• for a permutation (or assignment) $\pi : \mathcal{B} \rightarrow \mathcal{R}$, there is an...

2. Optimal transport, wave functions and single electron densities

Prof. Luigi De Pascale (Università degli Studi di Firenze)

26/11/2021, 15:15

I will discuss some properties of the mapping from wave-functions to single particle densities. In particular I will show that in some case this mapping is open.
The tool will be the construction of special transport plans with given marginals. This partially answers an open question of E.H. Lieb. (From a joint work with Ugo Bindini).

3. There is no invariant cyclically monotone Poisson matching in 2d

Prof. Francesco Mattesini (University of Münster)

26/11/2021, 16:00

The optimal matching problem is a classical random variational problem that received interest in the last 30 years. We show that there exists no cyclically monotone invariant matching of two independent Poisson processes in the critical dimension $d=2$. Our argument relies on a recent harmonic approximation theorem together with the two-dimensional local asymptotics for the bipartite matching...

4. Optimal quantization strategies for vectorial signals

Prof. Eugene Stepanov (Steklov Institute of Mathematics, St. Petersburg)

26/11/2021, 16:45

We will discuss and compare two approaches for quantization of vectorial signals on the input to a computational device: quantizing the whole signal and optimizing the input error, or quantizing separately the components
but optimizing the output error.