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...
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...
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...
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...
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)
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)
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...
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)
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)
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)
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)
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)
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)
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)
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...
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...
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...
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...
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...
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...
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...
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...
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)
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)
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...
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)
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)
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)
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)
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)
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)
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...