Scaling limit for a neuron-firing network model

Abstract

The Brownian web can be roughly described as a family of coalescing one-dimensional Brownian motions starting at all times in ℝ and at all points of ℝ. In this paper, we only consider starting times which are nonnegative, that is, all the space-time points in ℝ× [0, ∞]; accordingly, we call it nonnegative Brownian web. Moreover, we introduce a model named neuron-firing network model and show that under diffusive scaling this model converges in distribution to the nonnegative Brownian Web.