Stability for the mailing problem

Maria Colombo
2019
Article

Résumé

We prove that optimal traffic plans for the mailing problem in Rd are stable with respect to variations of the given coupling, above the critical exponent α=1−1/d, thus solving an open problem stated in the book Optimal transportation networks, by Bernot, Caselles and Morel. We apply our novel result to study some regularity properties of the minimizers of the mailing problem, showing that only finitely many connected components of an optimal traffic plan meet together at any branching point.

Source officielle

https://infoscience.epfl.ch/record/274614?ln=fr

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Critical values in an anisotropic percolation on $\mathbb{Z}^2$

Hao Xue

In this thesis, we consider an anisotropic finite-range bond percolation model on

\mathbb{Z}^2

. On each horizontal layer

\{(x,i):x\in\mathbb{Z}\}

for

i\in\mathbb{Z}

, we have edges

\langle(x,i),(y,i)\rangle

for

1\leq|x-y|\leq N

with $N\in\mathbb{N ...

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Stability for the mailing problem

Critical values in an anisotropic percolation on $\mathbb{Z}^2$

Lifshitz point at commensurate melting of chains of Rydberg atoms

Critical values in an anisotropic percolation on $\mathbb{Z}^2$

Lifshitz point at commensurate melting of chains of Rydberg atoms