In this paper, we present a new model of dendrite growth in battery cells through theoretical and numerical analysis. We use a statistical model based on the competition between a deterministic electric field and a stochastic force, which both drive the movement of the particles inside the battery cell. The simulation of the dendrite growth is modeled via Diffusion Limited Aggregation. As a major aspect, we point out the key role played by the intense electric field close to the edges of the electrodes, which statistically drives the particles along the electric field lines.