Related papers: Large deviations for conditional guesswork

A source sequence is to be guessed with some fidelity based on a rate-limited description of an observed sequence with which it is correlated. The trade-off between the description rate and the exponential growth rate of the least power…

The guesswork is an information-theoretic quantity which can be seen as an alternate security criterion to entropy. Recent work has established the theoretical framework for guesswork in the presence of quantum side information, which we…

Scaling inference compute in large language models (LLMs) through repeated sampling consistently increases the coverage (fraction of problems solved) as the number of samples increases. We conjecture that this observed improvement is…

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…

We study the greedy independent set algorithm on sparse Erd\H{o}s-R\'enyi random graphs ${\mathcal G}(n,c/n)$. This range of $p$ is of interest due to the threshold at $c=e$, beyond which it appears that greedy algorithms are affected by a…

The Airy point process is a determinantal point process that arises from the spectral edge of the Gaussian Unitary Ensemble. In this paper, we establish a large deviation principle for the Airy point process. Our result also extends to…

The estimation of the guessing probability has paramount importance in quantum cryptographic processes. It can also be used as a witness for nonlocal correlations. In most of the studied scenarios, estimating the guessing probability…

We extend the Erd\H os-R\' enyi law of large numbers to the averaging setup both in discrete and continuous time cases. We consider both stochastic processes and dynamical systems as fast motions whenever they are fast mixing and satisfy…

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…

We study a precise large deviation principle for a stationary regularly varying sequence of random variables. This principle extends the classical results of A.V. Nagaev (1969) and S.V. Nagaev (1979) for iid regularly varying sequences. The…

A large deviations principle is established for the joint law of the empirical measure and the flow measure of a renewal Markov process on a finite graph. We do not assume any bound on the arrival times, allowing heavy tailed distributions.…

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…

Large language models make remarkable progress in reasoning capabilities. Existing works focus mainly on deductive reasoning tasks (e.g., code and math), while another type of reasoning mode that better aligns with human learning, inductive…

We investigate large deviations for the empirical measure of the position and momentum of a particle traveling in a box with hot walls. The particle travels with uniform speed from left to right, until it hits the right boundary. Then it 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 paper concerns itself with establishing large deviation principles for a sequence of stochastic integrals and stochastic differential equations driven by general semimartingales in infinite-dimensional settings. The class of…

We study large deviations from the invariant measure for nonlinear Schr\"odinger equations with colored noises on determining modes. The proof is based on a new abstract criterion, inspired by [V. Jak\v{s}i\'{c} et al., Comm. Pure Appl.…

We revisit the problem of statistical sequence matching initiated by Unnikrishnan (TIT 2015) and derive theoretical performance guarantees for sequential tests that have bounded expected stopping times. Specifically, in this problem, one is…

We prove a large deviation principle for the point process of large Poisson $k$-nearest neighbor balls in hyperbolic space. More precisely, we consider a stationary Poisson point process of unit intensity in a growing sampling window in…

Gaussian couplings of partial sum processes are derived for the high-dimensional regime $d=o(n^{1/3})$. The coupling is derived for sums of independent random vectors and subsequently extended to nonstationary time series. Our inequalities…