Christophe Sabot

A probabilistic representation of constants in Kesten's renewal theorem (2008)

Enriquez, Nathanaël, Sabot, Christophe, Zindy, Olivier

The aims of this paper are twofold. Firstly, we derive some probabilistic representation for the constant which appears in the one-dimensional case of Kesten's renewal theorem. Secondly, we estimate...

A probabilistic representation of constants in Kesten's renewal theorem (2008)

Enriquez, Nathanaël, Sabot, Christophe, Zindy, Olivier

The aims of this paper are twofold. Firstly, we derive some probabilistic representation for the constant which appears in the one-dimensional case of Kesten's renewal theorem. Secondly, we estimate...

Renewal series and square-root boundaries for Bessel processes (2008)

Enriquez, Nathanael, Sabot, Christophe, Yor, Marc

We show how a description of Brownian exponential functionals as a renewal series gives access to the law of the hitting time of a square-root boundary by a Bessel process. This extends classical...

Renewal series and square-root boundaries for Bessel processes (2008)

Enriquez, Nathanael, Sabot, Christophe, Yor, Marc

We show how a description of Brownian exponential functionals as a renewal series gives access to the law of the hitting time of a square-root boundary by a Bessel process. This extends classical...

Renewal series and square-root boundaries for Bessel processes (2008)

Enriquez, Nathanael, Sabot, Christophe, Yor, Marc

We show how a description of Brownian exponential functionals as a renewal series gives access to the law of the hitting time of a square-root boundary by a Bessel process. This extends classical...

Limit laws for transient random walks in random environment on $\z$ (2008)

Enriquez, Nathanaël, Sabot, Christophe, Zindy, Olivier

We consider transient random walks in random environment on $\z$ with zero asymptotic speed. A classical result of Kesten, Kozlov and Spitzer says that the hitting time of the level $n$ converges in...

Aging and quenched localization for one-dimensional random walks in random environment in the sub-ballistic regime (2008)

Enriquez, Nathanaël, Sabot, Christophe, Zindy, Olivier

We consider transient one-dimensional random walks in random environment with zero asymptotic speed. An aging phenomenon involving the generalized Arcsine law is proved using the localization of the...

Limit laws for transient random walks in random environment on $\z$ (2008)

Enriquez, Nathanaël, Sabot, Christophe, Zindy, Olivier

We consider transient random walks in random environment on $\z$ with zero asymptotic speed. A classical result of Kesten, Kozlov and Spitzer says that the hitting time of the level $n$ converges in...

Aging and quenched localization for one-dimensional random walks in random environment in the sub-ballistic regime (2008)

Enriquez, Nathanaël, Sabot, Christophe, Zindy, Olivier

We consider transient one-dimensional random walks in random environment with zero asymptotic speed. An aging phenomenon involving the generalized Arcsine law is proved using the localization of the...

Stokes matrices of hypergeometric integrals (2007)

Glutsyuk, Alexey, Sabot, Christophe

In this work we compute the Stokes matrices of the ordinary differential equation satisfied by the hypergeometric integrals associated to an arrangement of hyperplanes in generic position. This...

Aging and quenched localization for one-dimensional random walks in random environment in the sub-ballistic regime (2007)

Enriquez, Nathanaël, Sabot, Christophe, Zindy, Olivier

We consider transient one-dimensional random walks in random environment with zero asymptotic speed. An aging phenomenon involving the generalized Arcsine law is proved using the localization of the...

Aging and quenched localization for one-dimensional random walks in random environment in the sub-ballistic regime (2007)

Enriquez, Nathanaël, Sabot, Christophe, Zindy, Olivier

We consider transient one-dimensional random walks in random environment with zero asymptotic speed. An aging phenomenon involving the generalized Arcsine law is proved using the localization of the...

Limit laws for transient random walks in random environment on $\z$ (2007)

Enriquez, Nathanaël, Sabot, Christophe, Zindy, Olivier

We consider transient random walks in random environment on $\z$ with zero asymptotic speed. A classical result of Kesten, Kozlov and Spitzer says that the hitting time of the level $n$ converges in...

Limit laws for transient random walks in random environment on $\z$ (2007)

Enriquez, Nathanaël, Sabot, Christophe, Zindy, Olivier

We consider transient random walks in random environment on $\z$ with zero asymptotic speed. A classical result of Kesten, Kozlov and Spitzer says that the hitting time of the level $n$ converges in...

Limit laws for transient random walks in random environment on $\z$ (2007)

Enriquez, Nathanaël, Sabot, Christophe, Zindy, Olivier

We consider transient random walks in random environment on $\z$ with zero asymptotic speed. A classical result of Kesten, Kozlov and Spitzer says that the hitting time of the level $n$ converges in...

A probabilistic representation of constants in Kesten's renewal theorem (2007)

Enriquez, Nathanaël, Sabot, Christophe, Zindy, Olivier

The aims of this paper are twofold. Firstly, we derive some probabilistic representation for the constant which appears in the one-dimensional case of Kesten's renewal theorem. Secondly, we estimate...

A probabilistic representation of constants in Kesten's renewal theorem (2007)

Enriquez, Nathanaël, Sabot, Christophe, Zindy, Olivier

The aims of this paper are twofold. Firstly, we derive some probabilistic representation for the constant which appears in the one-dimensional case of Kesten's renewal theorem. Secondly, we estimate...

A probabilistic representation of constants in Kesten's renewal theorem (2007)

Enriquez, Nathanaël, Sabot, Christophe, Zindy, Olivier

The aims of this paper are twofold. Firstly, we derive some probabilistic representation for the constant which appears in the one-dimensional case of Kesten's renewal theorem. Secondly, we estimate...

Spectral Analysis of a Self-Similar Sturm-Liouville Operator (2006)

Sabot, Christophe

In this text we describe the spectral nature (pure point or continuous) of a self-similar Sturm-Liouville operator on the line or the half-line. This is motivated by the more general problem of...

Ballistic random walks in random environment at low disorder (2006)

Sabot, Christophe

We consider random walks in a random environment of the type p_0+\gamma\xi_z, where p_0 denotes the transition probabilities of a stationary random walk on \BbbZ^d, to nearest neighbors, and \xi_z is...

Electrical Networks, Symplectic Reductions, and Application to the Renormalization Map of Self-Similar Lattices (2006)

Sabot, Christophe

The first part of this paper deals with electrical networks and symplectic reductions. We consider two operations on electrical networks (the "trace map" and the "gluing map") and show that they...

Schr\"odinger operators on fractal lattices with random blow-ups (2006)

Sabot, Christophe

Starting from a finitely ramified self-similar set $X$ we can construct an unbounded set $X_{}$ by blowing-up the initial set $X$. We consider random blow-ups and prove elementary properties of the...

Spectral properties of self-similar lattices and iteration of rational maps (2006)

Sabot, Christophe

In this text we consider discrete Laplace operators defined on lattices based on finitely-ramified self-similar sets, and their continuous analogous defined on the self-similar sets themselves. We...

Random walks in a Dirichlet environment (2006)

Sabot, Christophe; Université Lyon 1; Csabot@umpa.ens-lyon.fr, Enriquez, Nathanaël; Université Paris 6; Enriquez@ccr.jussieu.fr

This paper states a law of large numbers for a random walk in a random iid environment on Zd, where the environment follows some Dirichlet distribution. Moreover, we give explicit bounds for the...

Markov chains in a Dirichlet Environment and hypergeometric integrals (2005)

Sabot, Christophe

The aim of this text is to establish some relations between Markov chains in Dirichlet Environments on directed graphs and certain hypergeometric integrals associated with a particular arrangement of...

Markov chains in a Dirichlet Environment and hypergeometric integrals (2005)

Sabot, Christophe

The aim of this text is to establish some relations between Markov chains in Dirichlet Environments on directed graphs and certain hypergeometric integrals associated with a particular arrangement of...

Markov chains in a Dirichlet Environment and hypergeometric integrals (2005)

Sabot, Christophe

The aim of this text is to establish some relations between Markov chains in Dirichlet Environments on directed graphs and certain hypergeometric integrals associated with a particular arrangement of...

Random walks in a Dirichlet environment (2005)

Enriquez, Nathanaël, Sabot, Christophe

This paper states a law of large numbers for a random walk in a random iid environment on ${\mathbb Z}^d$, where the environment follows some Dirichlet distribution. Moreover, we give explicit bounds...

Markov chains in a Dirichlet Environment and hypergeometric integrals (2005)

Sabot, Christophe

The aim of this text is to establish some relations between Markov chains in Dirichlet Environments on directed graphs and certain hypergeometric integrals associated with a particular arrangement of...

Markov chains in a Dirichlet Environment and hypergeometric integrals (2005)

Sabot, Christophe

The aim of this text is to establish some relations between Markov chains in Dirichlet Environments on directed graphs and certain hypergeometric integrals associated with a particular arrangement of...

Random walks in a Dirichlet environment (2005)

Enriquez, Nathanaël, Sabot, Christophe

This paper states a law of large numbers for a random walk in a random iid environment on ${\mathbb Z}^d$, where the environment follows some Dirichlet distribution. Moreover, we give explicit bounds...

Random walks in a Dirichlet environment (2005)

Enriquez, Nathanaël, Sabot, Christophe

This paper states a law of large numbers for a random walk in a random iid environment on ${\mathbb Z}^d$, where the environment follows some Dirichlet distribution. Moreover, we give explicit bounds...

Random walks in a Dirichlet environment (2005)

Enriquez, Nathanaël, Sabot, Christophe

This paper states a law of large numbers for a random walk in a random iid environment on ${\mathbb Z}^d$, where the environment follows some Dirichlet distribution. Moreover, we give explicit bounds...

Boundary Value Problems in Some Ramified Domains with a Fractal Boundary: Analysis and Numerical Methods. Part II: Non homogeneous Neumann Problems. (2004)

Achdou, Yves, Sabot, Christophe, Tchou, Nicoletta

This paper is devoted to numerical methods for solving Poisson problems in self-similar ramified domains of $\R^2$ with a fractal boundary. It is proved that a sequence of solutions to some...

Boundary Value Problems in Some Ramified Domains with a Fractal Boundary: Analysis and Numerical Methods. Part I: Diffusion and Propagation problems. (2004)

Achdou, Yves, Sabot, Christophe, Tchou, Nicoletta

This paper is devoted to numerical methods for solving boundary value problems in self-similar ramified domains of $\R^2$ with a fractal boundary. Homogeneous Neumann conditions are imposed on the...

Boundary Value Problems in Some Ramified Domains with a Fractal Boundary: Analysis and Numerical Methods. Part II: Non homogeneous Neumann Problems. (2004)

Achdou, Yves, Sabot, Christophe, Tchou, Nicoletta

This paper is devoted to numerical methods for solving Poisson problems in self-similar ramified domains of $\R^2$ with a fractal boundary. It is proved that a sequence of solutions to some...

Boundary Value Problems in Some Ramified Domains with a Fractal Boundary: Analysis and Numerical Methods. Part I: Diffusion and Propagation problems. (2004)

Achdou, Yves, Sabot, Christophe, Tchou, Nicoletta

This paper is devoted to numerical methods for solving boundary value problems in self-similar ramified domains of $\R^2$ with a fractal boundary. Homogeneous Neumann conditions are imposed on the...

Boundary Value Problems in Some Ramified Domains with a Fractal Boundary: Analysis and Numerical Methods. Part II: Non homogeneous Neumann Problems. (2004)

Achdou, Yves, Sabot, Christophe, Tchou, Nicoletta

This paper is devoted to numerical methods for solving Poisson problems in self-similar ramified domains of $\R^2$ with a fractal boundary. It is proved that a sequence of solutions to some...

Boundary Value Problems in Some Ramified Domains with a Fractal Boundary: Analysis and Numerical Methods. Part I: Diffusion and Propagation problems. (2004)

Achdou, Yves, Sabot, Christophe, Tchou, Nicoletta

This paper is devoted to numerical methods for solving boundary value problems in self-similar ramified domains of $\R^2$ with a fractal boundary. Homogeneous Neumann conditions are imposed on the...

Boundary Value Problems in Some Ramified Domains with a Fractal Boundary: Analysis and Numerical Methods. Part II: Non homogeneous Neumann Problems. (2004)

Achdou, Yves, Sabot, Christophe, Tchou, Nicoletta

This paper is devoted to numerical methods for solving Poisson problems in self-similar ramified domains of $\R^2$ with a fractal boundary. It is proved that a sequence of solutions to some...

Boundary Value Problems in Some Ramified Domains with a Fractal Boundary: Analysis and Numerical Methods. Part I: Diffusion and Propagation problems. (2004)

Achdou, Yves, Sabot, Christophe, Tchou, Nicoletta

This paper is devoted to numerical methods for solving boundary value problems in self-similar ramified domains of $\R^2$ with a fractal boundary. Homogeneous Neumann conditions are imposed on the...

Ballistic random walks in random environment at low disorder (2004)

Sabot, Christophe

We consider random walks in a random environment of the type p0+γξz, where p0 denotes the transition probabilities of a stationary random walk on ℤd, to nearest neighbors, and ξz is an i.i.d....

Spectral Analysis of a Self-Similar Sturm-Liouville Operator (2004)

Sabot, Christophe

In this text we describe the spectral nature (pure point or continuous) of a self-similar Sturm-Liouville operator on the line or the half-line. This is motivated by the more general problem of...

Electrical Networks, Symplectic Reductions, and Application to the Renormalization Map of Self-Similar Lattices (2003)

Sabot, Christophe

The first part of this paper deals with electrical networks and symplectic reductions. We consider two operations on electrical networks (the "trace map" and the "gluing map") and show that they...

Symplectic Geometrical Aspects of the (2003)

Christophe Sabot

We present the renormalization map we introduced in [23] in order to describe the spectral properties of self-similar lattices, from the point of view of symplectic geometry. We show that this map...

Ballistic random walks in random environment at low disorder (2003)

Sabot, Christophe

We consider random walks in a random environment of the type p_0+\gamma\xi_z, where p_0 denotes the transition probabilities of a stationary random walk on \BbbZ^d, to nearest neighbors, and \xi_z is...

Spectral properties of self-similar lattices and iteration of rational maps (2002)

Sabot, Christophe

In this text we consider discrete Laplace operators defined on lattices based on finitely-ramified self-similar sets, and their continuous analogous defined on the self-similar sets themselves. We...

Schr\"odinger operators on fractal lattices with random blow-ups (2002)

Sabot, Christophe

Starting from a finitely ramified self-similar set $X$ we can construct an unbounded set $X_{}$ by blowing-up the initial set $X$. We consider random blow-ups and prove elementary properties of the...

Spectral Properties of Hierarchical Lattices (2001)

Christophe Sabot

In this text we are interested in spectral properties of discrete Laplace operators defined on lattices based on finitely-ramified self-similar sets. The basic example is the lattice based on the...

Schrodinger Operators on Fractal Lattices (2001)

Christophe Sabot

Starting from a finitely ramified self-similar set X we can construct an unbounded set X!1? by blowing-up the initial set X. We consider random blow-ups and prove elementary properties of the...