Polynomial localization of the 2D-Vertex Reinforced Jump Process

We prove polynomial decay of the mixing field Vertex Reinforced Jump Process (VRJP) on ${\mathbb {Z}}^{2}$ with bounded conductances. Using [22] we deduce that VRJP any constant conductances is almost surely recurrent. It gives a counterpart result Merkl, Rolles [16] and Sabot, Zeng for 2-dimensional Edge Random Walk.