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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 temperature

Nature: Original

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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 forms

Nature: Original

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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

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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

Chaos multiplicatif : un traitement simple et complet de la fonction de partition (Statistical mechanics)

Introduced by Mandelbrot (

Keywords: Multiplicative chaos, Partition function, Pressure, Critical temperature

Nature: Original

Retrieve article from Numdam

XXXI: 05, 54-61, LNM 1655 (1997)

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 forms

Nature: Original

Retrieve article from Numdam

XXXV: 16, 206-219, LNM 1755 (2001)

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)

Enroulements browniens et subordination dans les groupes de Lie

XLVI: 04, 71-103, LNM 2123 (2014)

Small Time Asymptotics for an Example of Strictly Hypoelliptic Heat Kernel (Stochastic analysis)

Nature: Original