In the model of catalytic branching random walk on \(\mathbb {Z}^d\) , we study the concentration of particles bounded by the population propagation front as time tends to infinity. We assume that the regime is supercritical (the Malthusian parameter is positive) and the tails of the random walk jump are light, i.e., the Cramér condition is fulfilled. Since, in this case, the front is known to spread asymptotically linearly in time, we consider the layers of particles behind the front which also grow linearly in time, but at a slower rate. We establish that the number of particles in a layer grows exponentially fast, although with an index smaller than the Malthusian parameter. Bibliography: 30 titles.
