Évènement

Date(s) : 05/04/2016   iCal
11h00 - 12h00

$In\; this\; talk\; I\; will\; introduce\; a\; new\; distance\; between\; nonnegative\; finite\; Borel\; measures\; in\; \$\backslash mathbb\{R\}^d\$\; with\; arbitrary\; masses.\; The\; distance\; is\; constructed\; by\; a\; Lagrangian\; variational\; approach\; (minimization\; of\; an\; action\; functional),\; which\; is\; similar\; to\; the\; celebrated\; Benamou-Brenier\; formula\; for\; the\; quadratic\; Kantorovich-Rubinstein-Wasserstein\; distance\; between\; probability\; measures.\; In\; contrast\; with\; the\; classical\; theory\; of\; optimal\; transportation\; for\; probability\; measures,\; we\; allow\; for\; mass\; variations\; and\; do\; not\; require\; decay\; at\; infinity.\; I\; will\; present\; several\; topological\; and\; geometrical\; properties\; of\; the\; resulting\; metric\; space.$
If time permits I will discuss the application to a reaction-diffusion fitness-driven model of population dynamics: once suitably interpreted as a gradient flow with respect to our metric, we show that the model satisfies exponential convergence to the unique steady state with explicit rates.
This is joint with D. Vorotnikov and S. Kondratyev (Univ. Coimbra).

https://www.math.tecnico.ulisboa.pt/~monsaingeon/

Catégories

• Séminaire