2025/03/19 by Janko Gravner, Alexander E. Holroyd, Gravner, Janko +5 · 1 citation
Computer Science · #Bayesian Methods and Mixture Models #FOS: Mathematics #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2503.15746
openalex publication_date 2025/03/19 · openalex created_date 2025/10/17 · openalex updated_date 2026/07/28
In the polluted modified bootstrap percolation model, sites in the square lattice are independently initially occupied with probability p or closed with probability q. A site becomes occupied at a subsequent step if it is not closed and has at least one occupied nearest neighbor in each of the two coordinates. We study the final density of occupied sites when p and q are both small. We show that this density approaches 0 if q≥ Cp2/log p-1 and 1 if q≤ p2/(log p-1)1+o(1). Thus we establish a logarithmic correction in the critical scaling, which is known not to be present in the standard model, settling a conjecture of Gravner and McDonald from 1997.