Publication

On large deviations regimes for random media models

Damien Gauthier
2007
Theses

Abstract

We investigate the behavior of probabilities of large deviations above the mean versus large deviations below the mean for random additive functionals in a variety of random media models. Among others, we treat the large deviations of the point-to-hyperplane first-passage percolation on Zd and both the last-passage and the first-passage oriented percolation in Zd-1 × Z+. We also consider the large deviations of the parabolic Anderson model with white noise potential with respect to the Lyapunov exponent of the model.

Official source

https://infoscience.epfl.ch/entities/publication/54ff822e-e342-4857-85e0-1a8f37d3ae74

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Damien Gauthier
2007
Theses

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/54ff822e-e342-4857-85e0-1a8f37d3ae74

About this result

Ontological neighbourhood

Statistics

Statistical inference: Mathematical statistics

Related concepts (15)

Large deviations theory

In probability theory, the theory of large deviations concerns the asymptotic behaviour of remote tails of sequences of probability distributions. While some basic ideas of the theory can be traced to Laplace, the formalization started with insurance mathematics, namely ruin theory with Cramér and Lundberg. A unified formalization of large deviation theory was developed in 1966, in a paper by Varadhan. Large deviations theory formalizes the heuristic ideas of concentration of measures and widely generalizes the notion of convergence of probability measures.

Standard deviation

In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the values are spread out over a wider range. Standard deviation may be abbreviated SD, and is most commonly represented in mathematical texts and equations by the lower case Greek letter σ (sigma), for the population standard deviation, or the Latin letter s, for the sample standard deviation.

Noise (electronics)

In electronics, noise is an unwanted disturbance in an electrical signal. Noise generated by electronic devices varies greatly as it is produced by several different effects. In particular, noise is inherent in physics and central to thermodynamics. Any conductor with electrical resistance will generate thermal noise inherently. The final elimination of thermal noise in electronics can only be achieved cryogenically, and even then quantum noise would remain inherent. Electronic noise is a common component of noise in signal processing.

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