Related papers: Growth of normalizing sequences in limit theorems …

We are interested in a fragmentation process. We observe fragments frozen when their sizes are less than $\epsilon$ ($\epsilon$ > 0). Is is known ([BM05]) that the empirical measure of these fragments converges in law, under some…

We provide a unified, probabilistic approach using renewal theory to derive some novel limits of sums for the normalized binomial coefficients and for the normalized Eulerian numbers. We also investigate some corresponding results for their…

Let $X=\{X_n: n\in\mathbb{N}\}$ be a linear process in which the coefficients are of the form $a_i=i^{-1}\ell(i)$ with $\ell$ being a slowly varying function at the infinity and the innovations are independent and identically distributed…

Random walk on changing graphs is considered. For sequences of finite graphs increasing monotonically towards a limiting infinite graph, we establish transition probability upper bounds. It yields sufficient transience criteria for simple…

We proved the so called complex bounds for multimodal, infinitely renormalizable analytic maps with bounded combinatorics: deep renormalizations have polynomial-like extensions with definite modulus. The complex bounds is the first step to…

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 focus…

We prove limit theorems for sums of randomly chosen random variables conditioned on the summands. We consider several versions of the corner growth setting, including specific cases of dependence amongst the summands and summands with heavy…

In this short note, we study the behaviour of a product of matrices with a simultaneous renormalization. Namely, for any sequence $(A\_n)\_{n\in \mathbb{N}}$ of $d\times d$ complex matrices whose mean $A$ exists and whose norms' means are…

In this article we present a Bernstein inequality for sums of random variables which are defined on a graphical network whose nodes grow at an exponential rate. The inequality can be used to derive concentration inequalities in…

We consider graphs with vertices of degree 1 or 2 and prove that the numbers of components of sizes 2 to q have a limit normal distribution for any q > 1. The result is also extended to multigraphs.

The first order difference equation induced by the sequence of maps on $ \mathbb{C} $ has Hyers-Ulam stability where the limit of the geometric average of growth rate is convergent and not equal to one. %The average growth rate is a…

We show that the distributional nature of soft theorems requires the soft limit expansion to take priority over the regulator expansion of Feynman loop integrals. We start the study of soft graviton theorems at loop level from this…

A large class of evolutionary processes can be modeled by a rule which involves self-replication of some physical quantity with a non local rescaling. I show that a class of such models are exactly solvable -- in the discrete as well as…

We consider exponential large deviations estimates for unbounded observables on uniformly expanding dynamical systems. We show that uniform expansion does not imply the existence of a rate function for unbounded observables no matter the…

Consider any Dirichlet series sum a_n/n^z with nonnegative coefficients a_n and finite sum function f(z)=f(x+iy) when x is greater than 1. Denoting the partial sum a_1+...+a_N by s_N, the paper gives the following necessary and sufficient…

Let $f_{s,k}(n)$ be the maximum possible number of $s$-term arithmetic progressions in a sequence $a_1<a_2<\ldots<a_n$ of $n$ integers which contains no $k$-term arithmetic progression. For all integers $k > s \geq 3$, we prove that…

We consider the general question of estimating decay of correlations for non-uniformly expanding maps, for classes of observables which are much larger than the usual class of Holder continuous functions. Our results give new estimates for…

In this paper we give an extension of the Birkhoff--Lewis theorem to some semilinear PDEs. Accordingly we prove existence of infinitely many periodic orbits with large period accumulating at the origin. Such periodic orbits bifurcate from…

We provide a Kingman-like Theorem for arbitrary finite measures and a version of Birkhoff's Theorem for bounded observable. As an application, we show that Birkhoff's limit exists for some continuous observable, in an example of Bowen.

We study about order of growth and hyper order of growth of non trivial solutions of second order linear differential equations, having restrictions in the coefficients. These restrictions involve notions of Yang's inequality, Borel…