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![]() Title:Contact Process on Interchange Process Conference:IMPMS 2026 Tags:contact process, exclusion process and Interacting particle systems Abstract: We introduce a model of epidemics among moving particles on any locally finite graph. At any time, each vertex either is empty, occupied by a healthy particle, or occupied by an infected particle. Infected particles recover at rate 1 and transmit the infection to healthy particles at neighboring vertices at rate $\lambda$. In addition, particles perform an interchange process with rate $\mathsf v$, that is, the states of adjacent vertices are swapped independently at rate $\mathsf v$, allowing the infection to spread also through the movement of infected particles. On the $d$-dimensional Euclidean lattice, we start with a single infected particle at the origin and with all the other vertices independently occupied by a healthy particle with probability $p$ or empty with probability $1-p$. We define $\lambda_c(\mathsf v,p)$ as the threshold value for $\lambda$ above which the infection persists with positive probability and analyze its asymptotic behavior as $\mathsf v \to \infty$ for fixed $p$. Contact Process on Interchange Process ![]() Contact Process on Interchange Process | ||||
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