Related papers: One-sided large deviations for the ground-state en…
We consider the Gaussian beta-ensemble when $\beta$ scales with $n$ the number of particles such that $\displaystyle{{n}^{-1}\ll \beta\ll 1}$. Under a certain regime for $\beta$, we show that the largest particle satisfies a large…
We consider mean-field vector spin glasses with self-overlap correction. The limit of free energy is known to be the Parisi formula, which is an infimum over matrix-valued paths. We decompose such a path into a Lipschitz matrix-valued path…
We establish upper bounds for the decay rate of the energy of the damped fractional wave equation when the averages of the damping coefficient on all intervals of a fixed length are bounded below. If the power of the fractional Laplacian,…
A new combinatorial, analytical approach to the ground-state energy problem of spin glasses with different concentrations of +/- J interactions is developed. The energy e_0 is expressed in terms of the fraction of broken bonds mu_0 and…
In this paper, we investigate the finite connectivity spin-glass problem. Our work is focused on the expansion around the point of infinite connectivity of the free energy of a spin glass on a graph with Poissonian distributed connectivity:…
The behavior of relativistic particles in an electric and/or magnetic field is considered in the general case when the direction of propagation may differ from the direction of the field. A special attention is paid to the spin splitting…
A well known description of superradiance from pointlike collections of many atoms involves the dissipative motion of a large spin. The pertinent ``superradiance master equation'' allows for a formally exact solution which we subject to a…
We study spin glasses on random lattices with finite connectivity. In the infinite connectivity limit they reduce to the Sherrington Kirkpatrick model. In this paper we investigate the expansion around the high connectivity limit. Within…
Identifying heterogeneous structures in glasses --- such as localized soft spots --- and understanding structure-dynamics relations in these systems remain major scientific challenges. Here we derive an exact expression for the local…
We consider vector spin glass models with self-overlap correction. Since the limit of free energy is an infimum, we use arguments analogous to those for generic models to show the following: 1) the averaged self-overlap converges; 2) the…
We introduce a hierarchical class of approximations of the random Ising spin glass in $d$ dimensions. The attention is focused on finite clusters of spins where the action of the rest of the system is properly taken into account. At the…
We provide a strategy to find in few elementary calculations the critical exponents of the overlaps for dilute spin glasses, in absence of external field. Such a strategy is based on the expansion of a suitably perturbed average of the…
We examined energy spectrums of some particular systems of binary spins. It is shown that the configuration space can be divided into classes, and in the limit the energy distributions in these classes can be approximated by the normal…
The objective of the present paper is to establish exponential large deviation inequalities, and to use them to show exponential concentration inequalities for the free energy of a polymer in general random environment, its rate of…
We introduce a lattice spin model where frustration is due to multibody interactions rather than quenched disorder in the Hamiltonian. The system has a crystalline ground state and below the melting temperature displays a dynamic behaviour…
A two-dimensional easy-plane ferromagnetic substrate, interacting with a dipolar tip which is magnetised perpendicular with respect to the easy plane is studied numerically by solving the Landau-Lifshitz Gilbert equation. The dipolar tip…
We study the large $N$-dimensional limit of the Hessian spectrum at the global minimum of some subclasses of the spherical mixed $p$-spin models. Specifically, we show that its empirical spectral measure converges in probability to a…
In open quantum systems with strong symmetries, the global scaled cumulant generating function (SCGF) is generally nonanalytic, so the G\"artner-Ellis theorem cannot directly yield the genuine large-deviation rate function. To address this…
We study large deviations in the Langevin dynamics, with damping of order $\e^{-1}$ and noise of order $1$, as $\e\downarrow 0$. The damping coefficient is assumed to be state dependent. We proceed first with a change of time and then, we…
We derive exponential bounds on probabilities of large deviations for "light tail" martingales taking values in finite-dimensional normed spaces. Our primary emphasis is on the case where the bounds are dimension-independent or nearly so.…