Related papers: A short proof of Feige's conjecture for identicall…
The problem of guessing a random string is revisited. A close relation between guessing and compression is first established. Then it is shown that if the sequence of distributions of the information spectrum satisfies the large deviation…
The extended de Finetti theorem characterizes exchangeable infinite random sequences as conditionally i.i.d. and shows that the apparently weaker distributional symmetry of spreadability is equivalent to exchangeability. Our main result is…
A simple class of chaotic systems in a random environment is considered and the fluctuation theorem is extended under the assumption of reversibility.
We present a short and self-contained proof of the choosability version of Brooks' theorem.
We first establish a general random Sperner lemma by presenting a completely new approach for the theory of $L^{0}$-simplicial subdivisions of $L^{0}$-simplexes. Based on this, we are able to achieve a new complete proof of the random…
We prove an effective version of the Oppenheim conjecture with a polynomial error rate. The proof is based on an effective equidistribution theorem which in turn relies on recent progress towards restricted projection problem.
We conjecture that the distribution of the edge-disjoint union of two random regular graphs on the same vertex set is asymptotically equivalent to a random regular graph of the combined degree, provided it grows as the number of vertices…
We prove a quantitative version of a Silverstein's Theorem on a condition for convergence in probability of the norm of random matrix. More precisely, we show that for a random matrix whose entries are i.i.d. random variables, $w_{i,j}$,…
We prove new results, related to the Littlewood and Mixed Littlewood conjectures in Diophantine approximation.
We prove a version of adelic descent for continuous localizing invariants.
A very short proof of the Fej\'er-Riesz lemma is presented in the matrix case
Recently Raayoni et al. announced various conjectures on continued fractions of fundamental constants automatically generated with machine learning techniques. In this paper we prove some of their stated conjectures for Euler number $e$ and…
We give a short and relatively elementary proof of the Hilton-Milner Theorem.
The article is devoted to the formulation and proof of the theorem on convergence with probability 1 of expansion of iterated Ito stochastic integrals of arbitrary multiplicity based on generalized multiple Fourier series converging in the…
We give a new short proof of the most simple relation between consecutive power sums of the first m positive integers.
We prove the numerical Hodge standard conjecture for the square of a simple abelian variety of prime dimension, and also in some related cases.
We consider the simple random walk on random graphs generated by discrete point processes. This random graph has a random subset of a cubic lattice as the vertices and lines between any consecutive vertices on lines parallel to each…
A new finite form of de Finetti's representation theorem is established using elementary information-theoretic tools. The distribution of the first $k$ random variables in an exchangeable vector of $n\geq k$ random variables is close to a…
In this note, we use the method of [3] to give a simple proof of famous Witten conjecture. Combining the coefficients derived in our note and this method, we can derive more recursion formulas of Hodge integrals.
Gibbs-type random probability measures and the exchangeable random partitions they induce represent an important framework both from a theoretical and applied point of view. In the present paper, motivated by species sampling problems, we…