Related papers: A second moment proof of the spread lemma
Fluctuation theorem is one of the major achievements in the field of nonequilibrium statistical mechanics during the past two decades. Steady-state fluctuation theorem of sample entropy production rate in terms of large deviation principle…
Network method of moments arXiv:1202.5101 is an important tool for nonparametric network inference. However, there has been little investigation on accurate descriptions of the sampling distributions of network moment statistics. In this…
We obtain two theorems extending the use of a saddlepoint approximation to multiparameter problems for likelihood ratio-like statistics which allow their use in permutation and rank tests and could be used in bootstrap approximations. In…
The celebrated dimension reduction lemma of Johnson and Lindenstrauss has numerous computational and other applications. Due to its application in practice, speeding up the computation of a Johnson-Lindenstrauss style dimension reduction is…
We construct a point set in the Euclidean plane that elucidates the relationship between the fine-scale statistics of the fractional parts of $\sqrt n$ and directional statistics for a shifted lattice. We show that the randomly rotated, and…
We develop a multidimensional Stein methodology for non-degenerate self-decomposable random vectors in $\mathbb{R}^d$ having finite first moment. Building on previous univariate findings, we solve an integro-partial differential Stein…
Expansions of the monadic second-order (MSO) theory of the structure $\langle \mathbb{N} ; < \rangle$ have been a fertile and active area of research ever since the publication of the seminal papers of B\"uchi and Elgot & Rabin on the…
A famous theorem of Szemer\'edi asserts that all subsets of the integers with positive upper density will contain arbitrarily long arithmetic progressions. There are many different proofs of this deep theorem, but they are all based on a…
We derive asymptotics for the moments as well as the weak limit of the height distribution of watermelons with p branches with wall. This generalises a famous result of de Bruijn, Knuth and Rice on the average height of planted plane trees,…
Let $\lambda(n)$ be the Liouville function. We study the distribution of \[ \frac{1}{x^{1/2}}\sum_{x\leq n\leq 2x}\lambda(f(n)) \] over random polynomials $f$ of fixed degree $d$ and coefficients bounded in magnitude by $H$. In particular…
Ultraslow diffusion (i.e. logarithmic diffusion) has been extensively studied theoretically, but has hardly been observed empirically. In this paper, firstly, we find the ultraslow-like diffusion of the time-series of word counts of already…
Elkies and McMullen [Duke Math.J.~123 (2004) 95--139] have shown that the gaps between the fractional parts of \sqrt n for n=1,\ldots,N, have a limit distribution as N tends to infinity. The limit distribution is non-standard and differs…
The well known bunkbed conjecture about percolation on finite graphs is now resolved; Gladkov, Pak and Zimin, building upon work of Hollom, have constructed a counterexample. We revisit this conjecture and study it in the broader context of…
We give a time-randomness tradeoff for the quasi-random rumor spreading protocol proposed by Doerr, Friedrich and Sauerwald [SODA 2008] on complete graphs. In this protocol, the goal is to spread a piece of information originating from one…
Green and Tao famously proved in 2005 that any subset of the primes of fixed positive density contains arbitrarily long arithmetic progressions. Green had previously shown that in fact any subset of the primes of relative density tending to…
The new field of adaptive data analysis seeks to provide algorithms and provable guarantees for models of machine learning that allow researchers to reuse their data, which normally falls outside of the usual statistical paradigm of static…
Let $X_1,X_2, \ldots $ be independent random uniform points in a bounded domain $A \subset \mathbb{R}^d$ with smooth boundary. Define the coverage threshold $R_n$ to be the smallest $r$ such that $A$ is covered by the balls of radius $r$…
We prove a formula for the evaluation of expectations containing a scalar function of a Gaussian random vector multiplied by a product of the random vector components, each one raised to a non-negative integer power. Some of the powers…
We derive asymptotics of moments and identify limiting distributions, under the random permutation model on m-ary search trees, for functionals that satisfy recurrence relations of a simple additive form. Many important functionals…
The axiomatic structure of the $\kappa$-statistcal theory is proven. In addition to the first three standard Khinchin--Shannon axioms of continuity, maximality, and expansibility, two further axioms are identified, namely the self-duality…