From transience to recurrence with Poisson tree frogs.

By Christopher E. Hoffman, Tobias Johnson, Matthew Junge. 2015

52 citations recorded by the source corpus.

Consider the following interacting particle system on the d-ary tree, known as the frog model: Initially, one particle is awake at the root and i.i.d. Poisson many particles are sleeping at every other vertex. Particles that are awake perform simple random walks, awakening any sleeping particles they encounter. We prove that there is a phase transition between transience and recurrence as the initial density of particles increases, and we give the order of the transition up to a logarithmic factor.

Subfields: Condensed Matter Physics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/ff2e057400f700d9da9588e60a8dc413be8c0fc2

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Condensed Matter Physics

1. Tobias Johnson
2. Christopher E. Hoffman
3. Matthew Junge

In Mathematical Physics

1. Tobias Johnson
2. Christopher E. Hoffman
3. Matthew Junge
4. F. Rassoul-Agha
5. Timo Seppäläinen
6. N. Georgiou
7. Michael Damron
8. Noam Berger

In Statistical and Nonlinear Physics

1. Tobias Johnson
2. Christopher E. Hoffman
3. Matthew Junge

Citations in the corpus

• Recurrence and transience for the frog model on trees (2014, methodology): “In this setting, we use the usual notion of stochastic dominance and a related bootstrapping argument to prove a phase transition from transience to recurrence on any d-ary tree as μ increases [14].”