An exactly solvable predator prey model with resetting

We study a simple model of a diffusing particle (the prey) that on encounter with one of a swarm of diffusing predators can either perish or be reset to its original position at the origin. We show that the survival probability of the prey up to time t decays algebraically as ∼t−θ(p,γ) where the exponent θ depends continuously on two parameters of the model, with p denoting the probability that a prey survives upon encounter with a predator and γ=DA/(DA+DB) where DA and DB are the diffusion constants of the prey and the predator respectively. We also compute exactly the probability distribution P(N|tc) of the total number of encounters till the capture time tc and show that it exhibits an anomalous large deviation form P(N|tc)∼t−Φ(Nlntc=z)c for large tc. The rate function Φ(z) is computed explicitly. Numerical simulations are in excellent agreement with our analytical results