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The frog model with drift on R
Consider a Poisson process on $\mathbb{R}$ with intensity $f$ where $0 \leq f(x)<\infty$ for ${x}\geq 0$ and ${f(x)}=0$ for $x<0$. The "points" of the process represent sleeping frogs. In addition,Expand
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The frog model on Galton-Watson trees
• Mathematics
• 6 October 2019
We consider an interacting particle system on trees known as the frog model: initially, a single active particle begins at the root and i.i.d. $\mathrm{Poiss}(\lambda)$ many inactive particles areExpand
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PR ] 6 F eb 2 01 7 The frog model with drift on R
Consider a Poisson process on R with intensity f where 0 ≤ f(x) < ∞ for x ≥ 0 and f(x) = 0 for x < 0. The “points” of the process represent sleeping frogs. In addition, there is one active frogExpand
Quenched Survival of Bernoulli Percolation on Galton-Watson Trees
• Mathematics
• 9 May 2018
We explore the survival function for percolation on Galton-Watson trees. Letting $g(T,p)$ represent the probability a tree $T$ survives Bernoulli percolation with parameter $p$, we establish severalExpand
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The frog model on non-amenable trees.
• Mathematics
• 11 October 2019
We examine an interacting particle system on trees commonly referred to as the frog model. For its initial state, it begins with a single active particle at the root and i.i.d.Expand
Maximal displacement of simple random walk bridge on Galton-Watson trees
We analyze simple random walk on a supercritical Galton-Watson tree, where the walk is conditioned to return to the root at time $2n$. Specifically, we establish the asymptotic order (up to aExpand
The nonhomogeneous frog model on ℤ
• Josh Rosenberg
• Mathematics, Computer Science
• Journal of Applied Probability
• 1 December 2018
We examine a system of interacting random walks with leftward drift on ℤ, which begins with a single active particle at the origin and some distribution of inactive particles on the positive integers. Expand
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Recurrence of the frog model on the 3,2-alternating tree
Consider a growing system of random walks on the 3,2-alternating tree, where generations of nodes alternate between having two and three children. Any time a particle lands on a node which has notExpand
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The nonhomogeneous frog model on $\mathbb{Z}$
We examine a system of interacting random walks with leftward drift on $\mathbb{Z}$, which begins with a single active particle at the origin and some distribution of inactive particles on theExpand
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