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Although deleting old edges in the uniformly grown graph changes abruptly the properties of the model, we show that some of the macro-characteristics of the graph vary continuously..
Figure 1: Three basically different posibilities in coupling continuous and discrete processes: in case ( a ) the continuous one moves while the discrete one does not change, in case
in the structure of large lattice animals of surface-area-to-volume ratio β is a combinatorial manifestation of the phase transition in percolation at criticality: a large
Although the exact convergence rate remains unknown for Wigner matrices, Bai and Yao [ 6 ] proved that the spectral empirical process of Wigner matrices indexed by a set of
The inequality (2) holds also for the more general setting of locally square integrable (continuous-parameter) martingales with bounded jumps (c.f. right-continuous with
We will first show that a Brownian bridge that is conditioned to avoid the origin has the same law as a Bessel bridge; and we will then note that the Bessel bridges have a density
Key words: Gaussian processes, processes indexed by trees, bounded processes, summation on trees, metric entropy.. AMS 2000 Subject Classification: Primary 60G15; Secondary:
Key words: bifurcating autoregressive process ; tree-indexed times series; martingales ; least squares estimation ; almost sure convergence ; quadratic strong law; central
