2025/10/06 by Nicolas Lanchier, Lanchier, Nicolas, Max Mercer +3 · 1 citation
Chemistry · #60K35 #Advanced Polymer Synthesis and Characterization #FOS: Mathematics #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2510.05397
openalex publication_date 2025/10/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper considers a natural variant of the d-dimensional multitype contact process in which individuals can be fertile or sterile. Fertile individuals of type i give birth to an offspring of their own type at rate λi, the offspring being fertile with probability pi and sterile with probability 1 - pi, whereas sterile individuals can't give birth. Offspring are sent to one of the neighbors of their parent's location and take place in the system if and only if the target site is empty. All the individuals die at rate one regardless of their type and regardless of whether they are fertile or sterile. Our main results show some qualitative disagreements between the spatial model and its nonspatial mean-field approximation that are more pronounced when the probability pi is small. More precisely, for the mean-field model, in the presence of only one type, survival occurs when λi pi > 1, and in the presence of two types, the type with the largest λi pi wins. In contrast, though the analysis of the spatial model shows a similar behavior when pi is close to one, in the presence of only one type, extinction always occurs when pi < 1/4d. Similarly, a type with λi > λc = critical value of the contact process and pi = 1 is more competitive than a type with λi arbitrarily large but pi < 1/4d, showing that the product λi pi no longer measures the competitiveness. These results underline the effects of space in the form of local interactions.