Related papers: What does a large deviation look like?
Complex systems are characterized by specific time-dependent interactions among their many constituents. As a consequence they often manifest rich, non-trivial and unexpected behavior. Examples arise both in the physical and non-physical…
We derive a general large deviation principle for a canonical sequence of probability measures, having its origins in random matrix theory, on unbounded sets $K$ of ${\bf C}$ with weakly admissible external fields $Q$ and very general…
Renewal processes with heavy-tailed power law distributed sojourn times are commonly encountered in physical modelling and so typical fluctuations of observables of interest have been investigated in detail. To describe rare events the rate…
Let $X$ be a L\'evy process with regularly varying L\'evy measure $\nu$. We obtain sample-path large deviations for scaled processes $\bar X_n(t) \triangleq X(nt)/n$ and obtain a similar result for random walks. Our results yield detailed…
Understanding realistic complex systems requires confronting significant conceptual, theoretical and experimental limitations rooted in the persistence of views that originated in the mechanics of simple moving bodies. We define the…
We present a dynamical theory of complex cooperative projects such as large engineering design or software development efforts, comprised of concurrent and interrelated tasks. The model accounts for temporal fluctuations both in task…
A system far from equilibrium is characterized by unconventional many-body dynamical effects, which can lead to anomalous density fluctuations and mass transport. Interestingly, these structural and dynamic features often emerge…
The large deviation principle is proved for a class of $L^2$-valued processes that arise from the coarse-graining of a random field. Coarse-grained processes of this kind form the basis of the analysis of local mean-field models in…
How do large deviation events in a stationary process cluster? The answer depends not only on the type of large deviations, but also on the length of memory in the process. Somewhat unexpectedly, it may also depend on the tails of the…
In many complex systems, large events are believed to follow power-law, scale-free probability distributions, so that the extreme, catastrophic events are unpredictable. Here, we study coupled chaotic oscillators that display extreme…
We revisit Wschebor's theorems on small increments for processes with scaling and stationary properties and deduce large deviation principles.
Elucidating the statistical properties of extreme meteo-climatic events and capturing the physical processes responsible for their occurrence are key steps for improving our understanding of climate variability and climate change and for…
We use a weak Gibbs property and a weak form of specification to derive level-2 large deviations principles for symbolic systems equipped with a large class of reference measures. This has applications to a broad class of symbolic systems,…
A phenomenological explanation is presented for the physics of aberration, which is in contrast with special relativity physics. The effect of relativity is identified with an effect due to the velocity of observation being affected by the…
The theory of large deviations constitutes a mathematical cornerstone in the foundations of Boltzmann-Gibbs statistical mechanics, based on the additive entropy $S_{BG}=- k_B\sum_{i=1}^W p_i \ln p_i$. Its optimization under appropriate…
In this paper, we establish a large deviation principle for the conservative stochastic partial differential equations, whose solutions are related to stochastic differential equations with interaction. The weak convergence method and the…
Time-irreversible stochastic processes are frequently used in natural sciences to explain non-equilibrium phenomena and to design efficient stochastic algorithms. Our main goal in this thesis is to analyse their dynamics by means of large…
We are trying to give a mathematically correct definition of outliers. Our approach is based on the distance between two last order statistics and appears to be connected to the law of large numbers. Key words: outliers, law of large…
The exact statistics of an arbitrary quantum observable is analytically obtained. Due to the probabilistic nature of a sequence of intermediate measurements and stochastic fluctuations induced by the interaction with the environment, the…
A proposal is made for a fundamental theory, in which the history of the universe is constituted of diverse views of itself. Views are attributes of events, and the theory's only be-ables; they comprise information about energy and momentum…