An Euclidean Random Assignment Problem (ERAP in short) is as follows:
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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);
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for a permutation (or assignment) $\pi : \mathcal{B} \rightarrow \mathcal{R}$, there is an...
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).
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...
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.
