Related papers: Large deviation principles for abelian monoids

The Erd\H{o}s-Kac theorem is a celebrated result in number theory which says that the number of distinct prime factors of a uniformly chosen random integer satisfies a central limit theorem. In this paper, we establish the large deviations…

We investigate the behaviour of a certain additive function depending on prime divisors of specific integers lying in large gaps between consecutive primes. The result is obtained by a combination of results and ideas related to large gaps…

We prove that if two additive functions (from a certain class) take large values with roughly the same probability then they must be identical. The Kac-Kubilius model suggests that the distribution of values of a given additive function can…

Large and moderate deviation principles are proved for Engel continued fractions, a new type of continued fraction expansion with non-decreasing partial quotients in number theory.

In this paper, we prove a large deviation principle of Freidlin-Wentzell's type for the multivalued stochastic differential equations. As an application, we derive a functional iterated logarithm law for the solutions of multivalued…

We derive a large deviation principle for the empirical measure of zeros of random polynomials with i.i.d. exponential coefficients.

For $0\le \alpha <1$ and $\beta>2$, we consider a linear mod 1 transformation on a unit interval; $x\mapsto\beta x+\alpha$ (${\rm mod}\ 1$), and prove that it satisfies the level-2 large deviation principle with the unique measure of…

We establish large deviation principles for the couple of the maximum likelihood estimators of dimensional and drift coefficients in the generalised squared radial Ornstein-Uhlenbeck process. We focus our attention to the most tractable…

We use the large deviation approach to sum rules pioneered by Gamboa, Nagel and Rouault to prove higher order sum rules for orthogonal polynomials on the unit circle. In particular, we prove one half of a conjectured sum rule of Lukic in…

Localized sufficient conditions for the large deviation principle of the given stochastic differential equations will be presented for stochastic differential equations with non-Lipschitzian and time-inhomogeneous coefficients, which is…

The link between Tauberian theorems and large deviations is surveyed, with particular reference to regular variation.

This paper establishs the large deviation principle (LDP) for multiple averages on $\mathbb{N}^d$. We extend the previous work of [Carinci et al., Indag. Math. 2012] to multidimensional lattice $\mathbb{N}^d$ for $d\geq 2$. The same…

In this paper, we establish the invariance principle and the large deviation for the biased random walk $RW_{\lambda}$ with $\lambda \in [0,1)$ on $\mathbb{Z}^d, d\geq 1$.

We prove pathwise large deviation principles of slow variables in slow-fast systems in the limit of time-scale separation tending to infinity. In the limit regime we consider, the convergence of the slow variable to its deterministic limit…

We establish the large deviation principle for a topological Markov shift over infinite alphabet which satisfies strong combinatorial assumptions called ``finite irreducibility'' or ``finite primitiveness''. More precisely, we assume the…

In this article we establish a large deviation principle for the family {\nu_{\epsilon}:\epsilon \in (0,1)} of distributions of the scaled stochastic processes {P_{-\log\sqrt{\epsilon}}Z_t}_{t\leq 1}, where (Z_t)_{t\in \lbrack 0,1]} is a…

We derive a general large deviation principle for a canonical sequence of probability measures, having its origins in random matrix theory, on unbounded sets $K$ of ${\bf C}$ with weakly admissible external fields $Q$ and very general…

In this article, we revisit the work of \cite{garrido2023large}, and prove large deviation principles for more general random initial data for cubic NLS. The Fourier coefficient of our random data admits an optimal polynomial decay.

Given an $n$-dimensional random vector $X^{(n)}$ , for $k < n$, consider its $k$-dimensional projection $\mathbf{a}_{n,k}X^{(n)}$, where $\mathbf{a}_{n,k}$ is an $n \times k$-dimensional matrix belonging to the Stiefel manifold…

We consider discrete $\beta$-ensembles as introduced by Borodin, Gorin and Guionnet in (Publications math{\' e}matiques de l'IH{\' E}S 125, 1-78, 2017). Under general assumptions, we establish a large deviation principle for their rightmost…