On common roots of random Bernoulli polynomials

TL;DR

This paper proves that as the degree grows, it is highly unlikely for d+1 random Bernoulli polynomials in d variables to share a common root, revealing a probabilistic property of polynomial systems.

Contribution

The paper establishes a high-probability result about the absence of common roots among random Bernoulli polynomial systems as degree increases.

Findings

High probability of no common roots for large degree

Asymptotic behavior of polynomial roots in random systems

Probabilistic bounds for polynomial root existence

Abstract

We prove that with high probability, d+1 random Bernoulli polynomials in d variables of degree n (n goes to infinity) do not possess a common root.