Related papers: Compact majority-minority districts almost never e…

We characterize the macroscopic attractor of infinite populations of noisy maps subjected to global and strong coupling by using an expansion in order parameters. We show that for any noise amplitude there exists a large region of strong…

We study random walk on topological full groups of subshifts, and show the existence of infinite, finitely generated, simple groups with the Liouville property. Results by Matui and Juschenko-Monod have shown that the derived subgroups of…

Conditions for almost sure extinction are studied in discrete time branching processes with an infinite number of types. It is not assumed that the expected number of children is a bounded function of the parent's type. There might also be…

For random piecewise linear systems T of the interval that are expanding on average we construct explicitly the density functions of absolutely continuous T-invariant measures. In case the random system uses only expanding maps our…

An electoral spoiler is usually defined as a losing candidate whose removal would affect the outcome by changing the winner. So far, spoiler effects have been analyzed primarily for single-winner electoral systems. We consider this subject…

We revisit the probabilistic construction of sparse random matrices where each column has a fixed number of nonzeros whose row indices are drawn uniformly at random with replacement. These matrices have a one-to-one correspondence with the…

We consider the problem of uniform sampling of points on an algebraic variety. Specifically, we develop a randomized algorithm that, given a small set of multivariate polynomials over a sufficiently large finite field, produces a common…

The traditional election control problem focuses on the use of control to promote a single candidate. In parliamentary elections, however, the focus shifts: voters care no less about the overall governing coalition than the individual…

We derive conditions under which random sequences of polarizations (two-point symmetrizations) converge almost surely to the symmetric decreasing rearrangement. The parameters for the polarizations are independent random variables whose…

We investigate the rank of random (symmetric) sparse matrices. Our main finding is that with high probability, any dependency that occurs in such a matrix is formed by a set of few rows that contains an overwhelming number of zeros. This…

Apportionment is the act of distributing the seats of a legislature among political parties (or states) in proportion to their vote shares (or populations). A famous impossibility by Balinski and Young (2001) shows that no apportionment…

We consider the task of estimating a conditional density using i.i.d. samples from a joint distribution, which is a fundamental problem with applications in both classification and uncertainty quantification for regression. For joint…

In our paper we study multiplicative properties of difference sets $A-A$ for large sets $A \subseteq \mathbb{Z}/q\mathbb{Z}$ in the case of composite $q$. We obtain a quantitative version of a result of A. Fish about the structure of the…

Let $q$ be a prime. We give an elementary proof of the fact that for any $k\in\mathbb{N}$, the proportion of $k$-element subsets of $\mathbb{Z}$ that contain a $q^{th}$ power modulo almost every prime, is zero. This result holds regardless…

We prove that any small enough neighborhood of a closed contact submanifold is always tight under a mild assumption on its normal bundle. The non-existence of $C^0$--small positive loops of contactomorphisms in general overtwisted manifolds…

Let $\mathbb{F}_p$ be the finite field of prime order $p$. For any function $f \colon \mathbb{F}_p{}^n \to \mathbb{F}_p$, there exists a unique polynomial over $\mathbb{F}_p$ having degree at most $p-1$ with respect to each variable which…

In this paper we prove that the cone $\PPD$ of positive, positive definite, discrete and strong almost periodic measures has an interesting property: given any positive and positive definite measure $\mu$ smaller than some measure in…

We consider expanding systems with invariant measures that are uniformly expanding everywhere except on a small measure set and show that the limiting statistics of hitting times for zero measure sets are compound Poisson provided the…

Let $Z_1,\, Z_2,\dots$ be independent and identically distributed complex random variables with common distribution $\mu$ and set $$ P_n(z) := (z - Z_1)\cdots (z - Z_n)\,. $$ Recently, Angst, Malicet and Poly proved that the critical points…

Let f:=(f^1,\...,f^n) be a sparse random polynomial system. This means that each f^i has fixed support (list of possibly non-zero coefficients) and each coefficient has a Gaussian probability distribution of arbitrary variance. We express…