Related papers: What does a large deviation look like?
What is the major difference between large and small systems? At small length-scales the dynamics is dominated by fluctuations, whereas at large scales fluctuations are irrelevant. Therefore, any thermodynamically consistent description of…
The theory of measurement is employed to elucidate the physical basis of general relativity. For measurements involving phenomena with intrinsic length or time scales, such scales must in general be negligible compared to the (translational…
We study the large deviations of sums of correlated random variables described by a matrix product ansatz, which generalizes the product structure of independent random variables to matrices whose non-commutativity is the source of…
There is growing effort in the "physics of behavior" that aims at complete quantitative characterization of animal movements under more complex, naturalistic conditions. One reaction to the resulting explosion of data is the search for low…
Large deviation principles are established for the two-parameter Poisson-Dirichlet distribution and two-parameter Dirichlet process when parameter $\theta$ approaches infinity. The motivation for these results is to understand the…
We analyse collective motion that occurs during rare (large deviation) events in systems of active particles, both numerically and analytically. We discuss the associated dynamical phase transition to collective motion, which occurs when…
A system driven in the vicinity of its critical point by varying a relevant field in an arbitrary function of time is a generic system that possesses a long relaxation time compared with the driving time scale and thus represents a large…
We study two problems. First, we consider the large deviation behavior of empirical measures of certain diffusion processes as, simultaneously, the time horizon becomes large and noise becomes vanishingly small. The law of large numbers…
Many natural systems are observed as point patterns in time, space, or space and time. Examples include plant and cellular systems, animal colonies, earthquakes, and wildfires. In practice the locations of the points are not always observed…
It is known that large deviations of sums of subexponential random variables are most likely realised by deviations of a single random variable. In this article we give a detailed picture of how subexponential random variables are…
We study rare events in systems of diffusive fields driven out of equilibrium by the boundaries. We present a numerical technique and use it to calculate the probabilities of rare events in one and two dimensions. Using this technique, we…
A quantitative theory, based on the Zeldovich approximation, to provide an approximate description of the evolution of structure is presented. We give an expression for the characteristic scale of superlarge-scale structure which can also…
A rigorous connection between large deviations theory and Gamma-convergence is established. Applications include representations formulas for rate functions, a contraction principle for measurable maps, a large deviations principle for…
The typical values and fluctuations of time-integrated observables of nonequilibrium processes driven in steady states are known to be characterized by large deviation functions, generalizing the entropy and free energy to nonequilibrium…
We propose a computational method for large deviation statistics of time-averaged quantities in general Markov processes. In our proposed method, we repeat a response measurement against external forces, where the forces are determined by…
Statistics of drawdowns (loss from the last local maximum to the next local minimum) plays an important role in risk assessment of investment strategies. As they incorporate higher ($>$ two) order correlations, they offer a better measure…
The configuration model is a sequence of random graphs constructed such that in the large network limit the degree distribution converges to a pre-specified probability distribution. The component structure of such random graphs can be…
We analyze the fluctuations of the dissipated energy in a simple and general model where dissipation, diffusion and driving are the key ingredients. The large deviation function for the dissipation follows from hydrodynamic fluctuation…
Extreme events are unusual and rare large-amplitude fluctuations that occur can unexpectedly in nonlinear dynamical systems. Events above the extreme event threshold of the probability distribution of a nonlinear process characterize…
The concept of typicality refers to properties holding for the "overwhelming majority" of cases and is a fundamental idea of the qualitative approach to dynamical problems. We argue that measure-theoretical typicality would be the adequate…