Critical density of activated random walks on transitive graphs

DOI10.1214/17-AOP1224zbMath1397.82038arXiv1512.02397MaRDI QIDQ1660631

Alexandre Stauffer, Lorenzo Taggi

Publication date: 16 August 2018

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1512.02397

zbMATH Keywords

random walksinteracting particle systemsabsorbing states phase transitions

Mathematics Subject Classification ID

Interacting particle systems in time-dependent statistical mechanics (82C22) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Dynamics of random walks, random surfaces, lattice animals, etc. in time-dependent statistical mechanics (82C41) Dynamic and nonequilibrium phase transitions (general) in statistical mechanics (82C26) Dynamic critical phenomena in statistical mechanics (82C27)

Related Items (15)

Brownian snails with removal: epidemics in diffusing populations ⋮ Uniform threshold for fixation of the stochastic sandpile model on the line ⋮ Bootstrap percolation, and other automata ⋮ Non-fixation for conservative stochastic dynamics on the line ⋮ Universality and sharpness in activated random walks ⋮ Sensitivity of the frog model to initial conditions ⋮ Diffusive bounds for the critical density of activated random walks ⋮ Essential enhancements in abelian networks: continuity and uniform strict monotonicity ⋮ Activated Random Walks on \(\mathbb{Z}^d\) ⋮ Active phase for activated random walk on \(\mathbb{Z}\) ⋮ Absorbing-state phase transition and activated random walks with unbounded capacities ⋮ Avalanches in critical activated random walks ⋮ Abelian oil and water dynamics does not have an absorbing-state phase transition ⋮ Activated random walk on a cycle ⋮ Active phase for activated random walks on \(\mathbb{Z}^d, d\geq3\), with density less than one and arbitrary sleeping rate

Cites Work

• Absorbing-state phase transition in biased activated random walk
• Absorbing-state phase transition for driven-dissipative stochastic dynamics on \(\mathbb Z\)
• Absorbing-state transition for stochastic sandpiles and activated random walks
• On fixation of activated random walks
• Activated random walkers: facts, conjectures and challenges
• Nonconcentration of return times
• Nonfixation for Activated Random Walks

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