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math.PR2016★ 1 cited
Convergence of complex martingales in the branching random walk: the boundary
Konrad Kolesko, Matthias Meiners
Biggins [Uniform convergence of martingales in the branching random walk. {\em Ann. Probab.}, 20(1):137--151, 1992] proved local uniform convergence of additive martingales in -…
math.PR2016
Local fluctuations of critical Mandelbrot cascades
Dariusz Buraczewski, Piotr Dyszewski, Konrad Kolesko
We investigate so-called generalized Mandelbrot cascades at the freezing (critical) temperature. It is known that, after a proper rescaling, a~sequence of multiplicative cascades c…