Year: 2006
Type: preprint
Abstract: We design a theoretic tree-based functional representation of a class of Feynman-Kac particle distributions, including an extension of the Wick product formula to interacting particle systems. These weak expansions rely on an original combinatorial, and permutation group analysis of a special class of forests. They provide refined non asymptotic propagation of chaos type properties, as well as sharp $\LL\_p$-mean error bounds, and laws of large numbers for $U$-statistics. Applications to particle interpretations of the top eigenvalues, and the ground states of Schrödinger semigroups are also discussed.
Source: arXiv (Cornell University)
Institution: Laboratoire Jean-Alexandre Dieudonné
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Agence Nationale de la Recherche
OpenAlex ID: W2951633871