Work

Broadcasting in random recursive dags

Year: 2025

Type: article

Abstract: A uniform k-DAG generalizes the uniform random recursive tree by picking k parents uniformly at random from the existing nodes. It starts with k “roots”. Each of the k roots is assigned a bit. These bits are propagated by a noisy channel. The parents’ bits are flipped with probability p, and a majority vote is taken. When all nodes have received their bits, the k-DAG is shown without identifying the roots. The goal is to estimate the majority bit among the roots. We identify the threshold for p as a function of k below which the majority rule among all nodes yields an error c + o(1) with c < 1/2. Above the threshold the majority rule errs with probability 1/2 + o(1).

Source: ESAIM Probability and Statistics

DOI: 10.1051/ps/2025002

Authors: Simon Briend, Luc Devroye, Gábor Lugosi

Institutions: UniDistance Suisse, McGill University, Institució Catalana de Recerca i Estudis Avançats, Universitat Pompeu Fabra, Barcelona School of Economics

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: