Two-type annihilating random walks on complete and star graphs have extinction times asymptotically larger than one-type annihilation, with near-matching upper and lower bounds for symmetric and asymmetric speeds.
Parking on transitive unimodular graphs
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abstract
Place a car independently with probability $p$ at each site of a graph. Each initially vacant site is a parking spot that can fit one car. Cars simultaneously perform independent random walks. When a car encounters an available parking spot it parks there. Other cars can still drive over the site, but cannot park there. For a large class of transitive and unimodular graphs, we show that the root is almost surely visited infinitely many times when $p \geq 1/2$, and only finitely many times otherwise.
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Two-type annihilating systems on the complete and star graph
Two-type annihilating random walks on complete and star graphs have extinction times asymptotically larger than one-type annihilation, with near-matching upper and lower bounds for symmetric and asymmetric speeds.