Related papers: An arithmetic regularity lemma, associated countin…
The gauge function, closely related to the atomic norm, measures the complexity of a statistical model, and has found broad applications in machine learning and statistical signal processing. In a high-dimensional learning problem, the…
We establish a Sewing lemma in the regime $\gamma \in \left( 0, 1 \right]$, constructing a Sewing map which is neither unique nor canonical, but which is nonetheless continuous with respect to the standard norms. Two immediate corollaries…
Obtaining an efficient bound for the triangle removal lemma is one of the most outstanding open problems of extremal combinatorics. Perhaps the main bottleneck for achieving this goal is that triangle-free graphs can be highly unstructured.…
We introduce a correspondence principle (analogous to the Furstenberg correspondence principle) that allows one to extract an infinite random graph or hypergraph from a sequence of increasingly large deterministic graphs or hypergraphs. As…
There have been, over the last 8 years, a number of far reaching extensions of the famous original F. and M. Riesz's uniqueness theorem that states that if a bounded analytic function in the unit disc of the complex plane $\Bbb C$ has the…
Many important statistical models fall outside classical moment-based methods due to the non-existence of moments or moment generating functions. We propose a generalised probabilistic framework in which densities are replaced by pairs…
Recent work of Gowers and Nagle, R\"odl, Schacht, and Skokan has established a hypergraph removal lemma, which in turn implies some results of Szemer\'edi and Furstenberg-Katznelson concerning one-dimensional and multi-dimensional…
Green developed an arithmetic regularity lemma to prove a strengthening of Roth's theorem on arithmetic progressions in dense sets. It states that for every $\epsilon > 0$ there is some $N_0(\epsilon)$ such that for every $N \ge…
The article presents a generalization of the classical Hardy-Littlewood conjecture concerning the density of prime tuples to the case of tuples consisting of almost-prime numbers (numbers with a specified quantity of prime divisors). The…
We develop a unified density-based framework for primality, coprimality, and prime pairs, and introduce an intrinsic normalized model for prime gaps constrained by the Prime Number Theorem. Within this setting, a structural tension between…
A major theme in arithmetic combinatorics is proving multiple recurrence results on semigroups (such as Szemer\'edi's theorem) and this can often be done using methods of ergodic Ramsey theory. What usually lies at the heart of such proofs…
In this work we consider a question in the calculus of variations motivated by riemannian geometry, the isoperimetric problem. We show that solutions to the isoperimetric problem, close in the flat norm to a smooth submanifold, are…
We aim to generalize the homogenisation theorem in \cite{Gehringer-Li-tagged} for a passive tracer interacting with a fractional Gau{\ss}ian noise to also cover fractional non-Gau{\ss}ian noises. To do so we analyse limit theorems for…
We prove a general quantitative theorem on the asymptotic behavior of stochastic quasi-Fej\'er monotone sequences in a broad metric context. Concretely, our result explicitly constructs a rate of convergence for such process, both in mean…
We give a proof of Szemeredi's regularity lemma in the special case of a graph with bounded VC dimension and show that it is possible to obtain "merely" doubly exponential bounds on the size of the partition in this case.
The logarithmic minimal models are not rational but, in the W-extended picture, they resemble rational conformal field theories. We argue that the W-projective representations are fundamental building blocks in both the boundary and bulk…
In this paper, we give a short proof of the weak convergence to the Kesten-McKay distribution for the normalized spectral measures of random $N$-lifts. This result is derived by generalizing a formula of Friedman involving Chebyshev…
In this paper, we examine regularity issues for two damped abstract elastic systems; the damping and coupling involve fractional powers $\mu, \theta$, with $0 \leq \mu , \theta \leq 1$, of the principal operators. The matrix defining the…
We first summarize the basic structure of the outer distribution module of a completely regular code. Then, employing a simple lemma concerning eigenvectors in association schemes, we propose to study the tightest case, where the indices of…
We consider distributions on a closed compact manifold $M$ as maps on smoothing operators. Thus spaces of certain maps between $\Psi^{-\infty}(M)\to \mathcal{C}^{\infty}(M)$ are considered as generalized functions. For any collection of…