XXIX: 18, 194-201, LNM 1613 (1995)
FRANCHI, Jacques
Chaos multiplicatif : un traitement simple et complet de la fonction de partition (
Statistical mechanics)
Introduced by Mandelbrot (
Comptes Rendus Acad. Sci. 278, 289--292, 1974), the model of multiplicative chaos has since been studied by several mathematicians and physicists. Using a trick of Kahane, this article presents a complete and elementary calculation of the pressure, thereby completing and simplifying previous work by Collet and Koukiou. Moreover it connects the critical temperature to the entropy, and gives a necessary and sufficient condition for finiteness of the critical temperature
Keywords: Multiplicative chaos,
Partition function,
Pressure,
Critical temperatureNature: Original
Retrieve article from Numdam
XXXI: 05, 54-61, LNM 1655 (1997)
FANG, Shizan;
FRANCHI, Jacques
A differentiable isomorphism between Wiener space and path group (
Malliavin's calculus)
The Itô map $I$ is known to realize a measurable isomorphism between Wiener space $W$ and the group ${\cal P}$ of paths with values in a Riemannian manifold. Here, the pullback $I^{*}$ is shown to be a diffeomorphism (in the sense of Malliavin derivatives) between the exterior algebras $\Lambda (W)$ and $\Lambda ({\cal P})$. This allows to transfer the Weitzenböck-Shigekawa identity from $\Lambda (W)$ to $\Lambda ({\cal P})$, yielding for example the de~Rham-Hodge-Kodaira decomposition on ${\cal P}$
Keywords: Wiener space,
Path group,
Brownian motion in a manifold,
Differential formsNature: Original Retrieve article from Numdam
XXXV: 16, 206-219, LNM 1755 (2001)
ENRIQUEZ, Nathanaël;
FRANCHI, Jacques;
LE JAN, Yves
Canonical lift and exit law of the fundamental diffusion associated with a Kleinian group Retrieve article from Numdam
XXXIX: 17, 357-380, LNM 1874 (2006)
ENRIQUEZ, Nathanaël;
FRANCHI, Jacques;
LE JAN, Yves
Enroulements browniens et subordination dans les groupes de Lie
XLVI: 04, 71-103, LNM 2123 (2014)
FRANCHI, Jacques
Small Time Asymptotics for an Example of Strictly Hypoelliptic Heat Kernel (
Stochastic analysis)
Nature: Original
