Brownian motion on the Sierpinski gasket
MT Barlow, EA Perkins - Probability theory and related fields, 1988 - Springer
We construct a “Brownian motion” taking values in the Sierpinski gasket, a fractal subset of ℝ
2, and study its properties. This is a diffusion process characterized by local isotropy and …
2, and study its properties. This is a diffusion process characterized by local isotropy and …
Branching processes. II
VA Vatutin, AM Zubkov - Journal of Soviet Mathematics, 1993 - Springer
The first part of our survey [64] was published in 1985. The long time that has elapsed has
prompted us to consider the second part not only as a continuation of the first, which treates …
prompted us to consider the second part not only as a continuation of the first, which treates …
Structure of shells in complex networks
J Shao, SV Buldyrev, LA Braunstein, S Havlin… - Physical Review E …, 2009 - APS
We define shell ℓ in a network as the set of nodes at distance ℓ with respect to a given node
and define r ℓ as the fraction of nodes outside shell ℓ. In a transport process, information or …
and define r ℓ as the fraction of nodes outside shell ℓ. In a transport process, information or …
[图书][B] Probabilistic methods for algorithmic discrete mathematics
Leave nothing to chance. This cliche embodies the common belief that ran domness has no
place in carefully planned methodologies, every step should be spelled out, each i dotted …
place in carefully planned methodologies, every step should be spelled out, each i dotted …
Large Deviation Rates for Branching Processes--I. Single Type Case
KB Athreya - The Annals of Applied Probability, 1994 - JSTOR
Let Zn∞ 0 be a Galton-Watson branching process with offspring distribution pj∞ 0. We
assume throughout that p0= 0, pj≠ 1 for any j≥ 1 and 1<m=Σjp_j<∞. Let Wn= Znm-m and …
assume throughout that p0= 0, pj≠ 1 for any j≥ 1 and 1<m=Σjp_j<∞. Let Wn= Znm-m and …
[HTML][HTML] Asymptotic properties and absolute continuity of laws stable by random weighted mean
Q Liu - Stochastic processes and their applications, 2001 - Elsevier
We study properties of stable-like laws, which are solutions of the distributional equation Z=
d∑ i= 1NA iZ i, where (N, A1, A2,…) is a given random variable with values in {0 …
d∑ i= 1NA iZ i, where (N, A1, A2,…) is a given random variable with values in {0 …
Branching processes and their applications in the analysis of tree structures and tree algorithms
L Devroye - Probabilistic methods for algorithmic discrete …, 1998 - Springer
We give a partial overview of some results from the rich theory of branching processes and
illustrate their use in the probabilistic analysis of algorithms and data structures. The …
illustrate their use in the probabilistic analysis of algorithms and data structures. The …
Large deviations in the supercritical branching process
JD Biggins, NH Bingham - Advances in Applied Probability, 1993 - cambridge.org
The tail behaviour of the limit of the normalized population size in the simple supercritical
branching process, W, is studied. Most of the results concern those cases when a tail of the …
branching process, W, is studied. Most of the results concern those cases when a tail of the …
Large deviations for branching processes in random environment
V Bansaye, J Berestycki - arXiv preprint arXiv:0810.4991, 2008 - arxiv.org
A branching process in random environment $(Z_n, n\in\N) $ is a generalization of Galton
Watson processes where at each generation the reproduction law is picked randomly. In this …
Watson processes where at each generation the reproduction law is picked randomly. In this …
Fractal boundaries of complex networks
We introduce the concept of the boundary of a complex network as the set of nodes at
distance larger than the mean distance from a given node in the network. We study the …
distance larger than the mean distance from a given node in the network. We study the …