相关论文: Large deviations for conditional guesswork
The second author studied arithmetic properties of a class of sequences that generalize the sequence of derangements. The aim of the following paper is to disprove two conjectures stated in \cite{miska}. The first conjecture regards the set…
Shot noise processes are used in applied probability to model a variety of physical systems in, for example, teletraffic theory, insurance and risk theory and in the engineering sciences. In this work we prove a large deviation principle…
We prove a maximal-type large deviation principle for dynamical systems with arbitrarily slow polynomial mixing rates. Also several applications, particularly to billiard systems, are presented.
We consider the general branching random walk under minimal assumptions, which in particular guarantee that the empirical particle distribution admits an almost sure central limit theorem. For such a process, we study the large time decay…
A computer code can simulate a system's propagation of variation from random inputs to output measures of quality. Our aim here is to estimate a critical output tail probability or quantile without a large Monte Carlo experiment. Instead,…
We study universal decoding over unknown discrete additive channels determined by a finite-state (unifilar) random process. Aiming at low-complexity decoders, we study variants of noise-guessing decoders that use estimators for the…
This work studies the deviations of the error exponent of the constant composition code ensemble around its expectation, known as the error exponent of the typical random code (TRC). In particular, it is shown that the probability of…
This note proves a law of large numbers for predicting several steps ahead, which, in the case of uniformly bounded random variables, generalizes the standard law of large numbers for martingales; the standard law of large numbers…
We consider a class of slow-fast processes on a connected complete Riemannian manifold $M$.The limiting dynamics as the scale separation goes to $\infty$ is governed by the averaging principle. Around this limit, we prove large deviation…
We consider the branching process in random environment $\{Z_n\}_{n\geq 0}$, which is a~population growth process where individuals reproduce independently of each other with the reproduction law randomly picked at each generation. We…
Given a multivariate big time series, can we detect anomalies as soon as they occur? Many existing works detect anomalies by learning how much a time series deviates away from what it should be in the reconstruction framework. However, most…
We study a system of interacting particles that randomly react to form new particles. The reaction flux is the rescaled number of reactions that take place in a time interval. We prove a dynamic large-deviation principle for the reaction…
We present here a simple method for computing the large deviation of long time average for stochastic jump processes. We show that the computation of the rate function can be reduced to that of a partial differential equation governing the…
Probabilistic programming languages allow programmers to write down conditional probability distributions that represent statistical and machine learning models as programs that use observe statements. These programs are run by accumulating…
Large deviations principle is obtained for terminating multidimensional compound renewal processes. We also obtained the asymptotic of large deviations for the case when a Gibbs change of the original probability measure takes place. The…
We consider a problem of guessing, wherein an adversary is interested in knowing the value of the realization of a discrete random variable $X$ on observing another correlated random variable $Y$. The adversary can make multiple (say, $k$)…
In this paper, we study the problem of determining $k$ anomalous random variables that have different probability distributions from the rest $(n-k)$ random variables. Instead of sampling each individual random variable separately as in the…
We investigate a Coulomb gas in a potential satisfying a weaker growth assumption than usual and establish a large deviation principle for its empirical measure. As a consequence the empirical measure is seen to converge towards a…
We study large deviations for measurable averaging operators on state spaces of dynamical systems. Our main motivation is the Hecke operators on the modular curve Y_0(p^n) and their generalization to higher rank S-arithmetic quotients. We…
We present a state-of-the-art model for fine-grained probability estimation of propositions conditioned on context. Recent advances in large language models (LLMs) have significantly enhanced their reasoning capabilities, particularly on…