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Limiting distribution of the rightmost particle in catalytic branching Brownian motion
2016
Electronic Communications in Probability
We study the model of binary branching Brownian motion with spatially-inhomogeneous branching rate βδ0(·), where δ0(·) is the Dirac delta function and β is some positive constant. We show that the distribution of the rightmost particle centred about β 2 t converges to a mixture of Gumbel distributions according to a martingale limit. Our results form a natural extension to S. Lalley and T. Sellke [10] for the degenerate case of catalytic branching. Before we state the main result of this
doi:10.1214/16-ecp22
fatcat:3g6zahwsybfd7fdlkdyvdma33y