Limiting Speed and Fluctuations for the Boundary Modified Contact Process

2025/12/04 by Heeszel, Andrew
#60K35 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2512.04431

Abstract

The boundary modified contact process models an epidemic spreading in one dimension with two infection parameters, λ_i and λ_e. Starting from a finite infected set, each edge of ℤ transmits the infection at rate λ_i except for the rightmost and leftmost edges incident to infected vertices, which transmit the infection at rate λ_e. We show a strong law of large numbers and central limit theorem for the location of the rightmost infected vertex when λ_i = λ_c and λ_e = λ_c + ε. We also show stretched exponential tail bounds in the fluctuations of the rightmost infected vertex, the extinction time of the process on the event of non-survival, and the probability of survival given the size of the initial infected region. Our results extend to the boundary modified contact process whenever λ_c ≤ λ_i < λ_e, and solves an open problem first proposed by Andjel and Rolla in [1].

Citations

• Dynamic Phenomena in Interacting Particle Systems: Phase Transitions and Equilibrium
• The box-crossing property for critical two-dimensional oriented percolation

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