A percolation representation is constructed for additive particle systems with finite distributive lattice state spaces, demonstrated on Krone's two-stage contact process.
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The voter model with dynamic anti-voter bonds is ergodic on every countable simple graph for arbitrary adoption kernels and all percolation parameters p and v.
α_c(v) converges to p_c as v → ∞, implying a non-trivial percolation phase transition for large v in the stirred voter model on Z^d, d ≥ 3.
A simplified version of Toom's Peierls argument based on Toom contours proves stability for monotone cellular automata with intrinsic randomness and derives lower bounds on critical parameters for deterministic automata.
Positive-rate probabilistic cellular automata admitting stationary Bernoulli measures are exponentially ergodic with logarithmic mixing times for finite regions.
citing papers explorer
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Percolation representations of additive particle systems
A percolation representation is constructed for additive particle systems with finite distributive lattice state spaces, demonstrated on Krone's two-stage contact process.
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Ergodicity of the voter model with dynamic anti-voter bonds
The voter model with dynamic anti-voter bonds is ergodic on every countable simple graph for arbitrary adoption kernels and all percolation parameters p and v.
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Percolation on the stationary distributions of the voter model with stirring
α_c(v) converges to p_c as v → ∞, implying a non-trivial percolation phase transition for large v in the stirred voter model on Z^d, d ≥ 3.
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Peierls bounds from Toom contours
A simplified version of Toom's Peierls argument based on Toom contours proves stability for monotone cellular automata with intrinsic randomness and derives lower bounds on critical parameters for deterministic automata.
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Positive-rate PCA and IPS with stationary Bernoulli measures are rapidly forgetful
Positive-rate probabilistic cellular automata admitting stationary Bernoulli measures are exponentially ergodic with logarithmic mixing times for finite regions.