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Quenched, annealed and functional large deviations for one-dimensional random walk in random environment

- F. Comets, N. Gantert, O. Zeitouni
- Mathematics
- 5 September 2000

Suppose that the integers are assigned random variables {ωi} (taking values in the unit interval), which serve as an environment. This environment defines a random walk {Xn} (called a RWRE) which,… Expand

Asymptotics for the survival probability in a killed branching random walk

- N. Gantert, Yueyun Hu, Zhan Shi
- Mathematics
- 3 November 2008

Considerons une marche aleatoire branchante surcritique a temps discret. Nous nous interessons a la probabilite qu'il existe un rayon infini du support de la marche aleatoire branchante, le long… Expand

The critical Branching Markov Chain is transient

- N. Gantert, Sebastian Mueller
- Mathematics
- 26 October 2005

We investigate recurrence and transience of Branching Markov Chains (BMC) in discrete time. Branching Markov Chains are clouds of particles which move (according to an irreducible underlying Markov… Expand

The maximum of a branching random walk with semiexponential increments

- N. Gantert
- Mathematics
- 1 June 2000

We consider an infinite Galton-Watson tree Γ and label the vertices υ with a collection of i.i.d. random variables (Y υ ) υ ∈ Γ . In the case where the upper tail of the distribution of Y υ is… Expand

Large deviations for weighted sums of stretched exponential random variables

- N. Gantert, K. Ramanan, Franz Rembart
- Mathematics
- 18 January 2014

We consider the probability that a weighted sum of n i.i.d. random variables $X_j, j = 1,\ldots,n$, with stretched exponential tails is larger than its expectation and determine the rate of its… Expand

Quenched Sub-Exponential Tail Estimates for One-Dimensional Random Walk in Random Environment

- N. Gantert, O. Zeitouni
- Mathematics
- 1 May 1998

Abstract:Suppose that the integers are assigned i.i.d. random variables {ωx} (taking values in the unit interval), which serve as an environment. This environment defines a random walk {Xn} (called a… Expand

Self-similarity of Brownian motion and a large deviation principle for random fields on a binary tree

- N. Gantert
- Mathematics
- 1 March 1994

SummaryUsing self-similarity of Brownian motion and its representation as a product measure on a binary tree, we construct a random sequence of probability measures which converges to the… Expand

Large deviations for random walks on Galton–Watson trees: averaging and uncertainty

- A. Dembo, N. Gantert, Y. Peres, O. Zeitouni
- Mathematics
- 1 February 2002

Abstract. In the study of large deviations for random walks in random environment, a key distinction has emerged between quenched asymptotics, conditional on the environment, and annealed… Expand

Large and moderate deviations for the local time of a recurrent Markov chain on ?2

- N. Gantert
- Mathematics
- 1 September 1998

Many visits to a single site by a transient random walk in random environment

- N. Gantert, Zhan Shi
- Mathematics
- 1 June 2002

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