# Criticality of a Randomly-Driven Front

@article{Dembo2017CriticalityOA, title={Criticality of a Randomly-Driven Front}, author={A. Dembo and Li-Cheng Tsai}, journal={Archive for Rational Mechanics and Analysis}, year={2017}, volume={233}, pages={643-699} }

AbstractConsider an advancing ‘front’ $${R(t) \in \mathbb{Z}_{\geqq 0}}$$R(t)∈Z≧0 and particles performing independent continuous time random walks on $${ (R(t), \infty) \cap \mathbb{Z}}$$(R(t),∞)∩Z. Starting at $${R(0)=0}$$R(0)=0, whenever a particle attempts to jump into $${R(t)}$$R(t) the latter instantaneously moves $${k \ge 1}$$k≥1 steps to the right, absorbing all particles along its path. We take k to be the minimal random integer such that exactly k particles are absorbed by the move of… CONTINUE READING

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