Papers › Improved critical drift estimates for the frog model on trees
Improved critical drift estimates for the frog model on trees
Poly Mathews Jr
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Place an active particle at the root of the infinite d-ary tree and dormant particles at each non-root site. Active particles move towards the root with probability p and otherwise move to a uniformly sampled child vertex. When an active particle moves to a site containing dormant particles, all the particles at the site become active. The critical drift p_d is the infimum over all p for which infinitely many particles visit the root almost surely. We give improved bounds on sup_(d ≥m) p_d and prove monotonicity of critical values associated to a self-similar variant.
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