Related papers: Tauberian theorems and large deviations
We establish a large-deviations principle for the largest eigenvalue of a generalized sample covariance matrix, meaning a matrix proportional to $Z^T \Gamma Z$, where $Z$ has i.i.d. real or complex entries and $\Gamma$ is not necessarily…
The relationship (both classical and quantum mechanical) between the discrete Liouville equation and Teichm\"uller theory is reviewed.
We discuss research done in two important areas of nonequilibrium statistical mechanics: fluctuation dissipation relations and dynamical fluctuations. In equilibrium systems the fluctuation-dissipation theorem gives a simple relation…
We discuss a recent line of research investigating inverse theorems with respect to general k-wise correlations, and explain how such correlations arise in different contexts in mathematics. We outline some of the results that were…
Higher order conformal perturbation theory is studied for theories with and without boundaries. We identify systematically the universal quantities in the beta function equations, and we give explicit formulae for the universal coefficients…
We study large deviation probabilities for a sum of dependent random variables from a heavy-tailed factor model, assuming that the components are regularly varying. We identify conditions where both the factor and the idiosyncratic terms…
Deep neural networks have achieved impressive results on a wide variety of tasks. However, quantifying uncertainty in the network's output is a challenging task. Bayesian models offer a mathematical framework to reason about model…
We make some observations connecting non-relativistic limits of string theory with $T\bar T$ deformations and TsT transformations.
In this paper we study the large deviations of time averaged mean square displacement (TAMSD) for Gaussian processes. The theory of large deviations is related to the exponential decay of probabilities of large fluctuations in random…
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 Sharp Large Deviations for Pearson's empirical correlation coefficients in the Spherical and Gaussian cases
We analyze the weak and critical points of various uncertainty relations that follow from the inequalities for the norms of vectors in the Hilbert space of states of a quantum system. There are studied uncertainty relations for sums of…
We announce a number of conjectures associated with and arising from a study of primes and irrationals in $\mathbb{R}$. All are supported by numerical verification to the extent possible.
This work concerns generalized backward stochastic differential equations, which are coupled with a family of reflecting diffusion processes. First of all, we establish the large deviation principle for forward stochastic differential…
A description of solutions of some integral equations has been obtained. A two-radii theorem is obtained as well.
In this paper we obtain some possibilistic variants of the probabilistic laws of large numbers, different from those obtained by other authors, but very natural extensions of the corresponding ones in probability theory. Our results are…
The Bell--Steinberger relation is analyzed. The questionable points of the standard derivation of this relation are discussed. It is shown that the use of a more accurate approximation than the one usually used in the derivation of this…
We develop a unified theory to analyze the microcanonical ensembles with several constraints given by unbounded observables. Several interesting phenomena that do not occur in the single constraint case can happen under the multiple…
Using the concept of constant evasion to different sorts of suitable binary relations, we establish many cardinal invariants derived from the established cardinal invariants $\mathfrak{e}^\mathrm{const}_{n}$ and…
The multifractal theory of turbulence uses a saddle-point evaluation in determining the power-law behaviour of structure functions. Without suitable precautions, this could lead to the presence of logarithmic corrections, thereby violating…