相关论文: Large Deviations and Random Energy Models

Multiple pendulums are investigated numerically and analytically to clarify the nonuniformity of average kinetic energies of particles. The nonuniformity is attributed to the system having constraints and it is consistent with the…

We analyze a pair of diffusion equations which are derived in the infinite system--size limit from a microscopic, individual--based, stochastic model. Deviations from the conventional Fickian picture are found which ultimately relate to the…

Random matrix theory yields valuable insights into the universal features of quantum many-body chaotic systems. Although all-to-all interactions are traditionally studied, many interesting dynamical questions, such as transport of a…

In this paper we address the problem of systems under an external feedback. This is performed using a large deviation approach and rate distortion from information theory. In particular we define a lower boundary for the maximum entropy…

In this paper, we consider the sublinear expectation on bounded random variables. With the notion of uncorrelatedness for random variables under the sublinear expectation, a weak law of large numbers is obtained. With the notion of…

Systematic inaccuracy is inherent in any computational estimate of a non-linear average, such as the free energy difference (Delta-F) between two states or systems, because of the availability of only a finite number of data values, N. In…

We analyze the large deviations for a discrete energy Kac-like walk. In particular, we exhibit a path, with probability exponentially small in the number of particles, that looses energy.

We analyze about two hundred naturally occurring networks with distinct dynamical origins to formally test whether the commonly assumed hypothesis of an underlying scale-free structure is generally viable. This has recently been questioned…

We prove a version of the completeness hypothesis that follows from the coexistence of symmetry and gravity: tree-level gravitational scattering mandates single-particle states in all possible irreducible representations of the symmetry…

Many models for complex phenomena use a model for strongly-interacting elements on a small scale to generate larger-scale simulations of some aspects of experimental realizations. These models may be agent-based (as in the case of discrete…

A basic result of large deviations theory is Sanov's theorem, which states that the sequence of empirical measures of independent and identically distributed samples satisfies the large deviation principle with rate function given by…

Electromagnetic mass models are proved to exist in higher dimensional theory of general relativity corresponding to charged dust distribution. Along with the general proof a specific example is also sited as a supporting candidate.

Let L be a positive line bundle over a projective complex manifold X. Consider the space of holomorphic sections of the tensor power of order p of L. The determinant of a basis of this space, together with some given probability measure on…

We introduce and analyze $d$ dimensional Coulomb gases with random charge distribution and general external confining potential. We show that these gases satisfy a large deviations principle. The analysis of the minima of the rate function…

A large deviation function mathematically characterizes the statistical property of atypical events. Recently, in non-equilibrium statistical mechanics, large deviation functions have been used to describe universal laws such as the…

One reason that free energy difference calculations are notoriously difficult in molecular systems is due to insufficient conformational overlap, or similarity, between the two states or systems of interest. The degree of overlap is…

We prove a full large deviations principle in large time, for a diffusion process with random drift V, which is a centered Gaussian shear flow random field. The large deviations principle is established in a ``quenched'' setting, i.e. is…

The omnipresent disorder in physical systems makes it imperative to investigate its effect on the spatial range of interactions for which system remains thermodynamically extensive. Previously known bounds on the statistical free energy for…

Large deviation results are given for a class of perturbed nonhomogeneous Markov chains on finite state space which formally includes some stochastic optimization algorithms. Specifically, let {P_n} be a sequence of transition matrices on a…

A formula to calculate the quantum fluctuations of energy in small subsystems of a hot and relativistic gas is derived. We find an increase in fluctuations for subsystems of small sizes, but we agrees with the energy fluctuations in the…