Related papers: A zero-one SUBEXP-dimension law for BPP
We introduce a probability distribution on $\mathcal{P}([0,1]^d)$, the space of all Borel probability measures on $[0,1]^d$. Under this distribution, almost all measures are shown to have infinite upper quasi-Assouad dimension and zero…
In this note we put forward a conjecture on the average optimal length for bipartite matching with a finite number of elements where the different lengths are independent one from the others and have an exponential distribution.
Given an irreducible sofic shift X, we show that an an irreducible SFT Y of lower entropy is a factor of X if and only if it is a factor of X by an open bi-continuing code. If these equivalent conditions hold and Y is mixing, then any code…
Suppose that we are given an infinite binary sequence which is random for a Bernoulli measure of parameter $p$. By the law of large numbers, the frequency of zeros in the sequence tends to~$p$, and thus we can get better and better…
In a recent paper, Bary-Soroker, Koukoulopoulos and Kozma proved that when $A$ is a random monic polynomial of $\mathbb{Z}[X]$ of deterministic degree $n$ with coefficients $a_j$ drawn independently according to measures $\mu_j,$ then $A$…
The phenomenon of superconvergence is proved for all freely infinitely divisible distributions. Precisely, suppose that the partial sums of a sequence of free identically distributed, infinitesimal random variables converge in distribution…
Conditional on the extended Riemann hypothesis, we show that with high probability, the characteristic polynomial of a random symmetric $\{\pm 1\}$-matrix is irreducible. This addresses a question raised by Eberhard in recent work. The main…
It is known that random monic integral polynomials of bounded degree $d$ and integral coefficients distributed uniformly and independently in $[-H,H]$ are irreducible over $\mathbb{Z}$ with probability tending to $1$ as $H\to \infty$. In…
The main results of this paper are twofold: the first one is a matrix theoretical result. We say that a matriz is superregular if all of its minors that are not trivially zero are nonzero. Given a a times b, a larger than or equal to b,…
Using an iterative tree construction we show that for simple computable subsets of the Cantor space Hausdorff, constructive and computable dimensions might be incomputable.
We show that a certain type of quasi finite, conservative, ergodic, measure preserving transformation always has a maximal zero entropy factor, generated by predictable sets. We also construct a conservative, ergodic, measure preserving…
An infinite bit sequence is called recursively random if no computable strategy betting along the sequence has unbounded capital. It is well-known that the property of recursive randomness is closed under computable permutations. We…
The main result is the following Theorem: Let p=p(n) be such that p(n) in [0,1] for all n and either p(n)<< n^{-1} or for some positive integer k, n^{-1/k}<< p(n)<< n^{-1/(k+1)} or for all epsilon >0, n^{- epsilon}<< p(n) and n^{-…
We consider uniformly continuous surjections between $C_p(X)$ and $C_p(Y)$ (resp, $C_p^*(X)$ and $C_p^*(Y$)) and show that if $X$ has some dimensional-like properties, then so does $Y$. In particular, we prove that if $T:C_p(X)\to C_p(Y)$…
This paper is devoted to the structure of the complete asymptotic expansion of the probability that a large combinatorial object is irreducible or consists of a given number of irreducible parts, where irreducibility is understood in terms…
We show that the BPS property is a generic feature of field theories in (1+1) dimensions, which does not put any restriction on the action. Here, by BPS solutions we understand static solutions which i) obey a lower-order Bogomolny-type…
In this paper we continue to explore infinitely renormalizable H\'enon maps with small Jacobian. It was shown in [CLM] that contrary to the one-dimensional intuition, the Cantor attractor of such a map is non-rigid and the conjugacy with…
A lower bound on the probability $P(0<X<\delta)$ for all real $\delta>0$ and all random variables $X$ with log-concave p.d.f.'s such that $EX=0$ and $EX^2=1$ is obtained.
In this paper we show that in systems where the probability distribution of the the overlap is non trivial in the infinity volume limit, the property of ultrametricity can be proved in general starting from two very simple and natural…
We prove that, for any Hausdorff continuum X, if dim X > 1 then the hyperspace C(X) of subcontinua of X is not a C-space; if dim X = 1 and X is hereditarily indecomposable then dim C(X) = 2 or C(X) is not a C-space. This generalizes results…