منابع مشابه
Power-law random walks.
In this paper, random walks with independent steps distributed according to a Q-power-law probability distribution function with Q=1/(1-q) are studied. In the case q>1, we show that (i) a stochastic representation of the location of the walk after n steps can be explicitly given (for both finite and infinite variance) and (ii) a clear connection with the superstatistics framework can be establi...
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We show that in power law random graphs, a.s., the expected rate at which a random walk with lookahead discovers the nodes of the graph is sublinear. Searching a graph by simulating a random walk is a natural way to abstract Web crawling [5]. Recently, the random walk simulation method has been also proposed to search P2P networks [11], [4], [10]. Therefore, it is important to characterize the ...
متن کاملPassage times of random walks and Lévy processes across power law boundaries
We establish an integral test involving only the distribution of the increments of a random walk S which determines whether lim supn→∞(Sn/n ) is almost surely zero, finite or infinite when 1/2 < κ < 1 and a typical step in the random walk has zero mean. This completes the results of Kesten and Maller [9] concerning finiteness of one-sided passage times over power law boundaries, so that we now ...
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The dynamics of many natural and artificial systems are well described as random walks on a network: the stochastic behaviour of molecules, traffic patterns on the internet, fluctuations in stock prices and so on. The vast literature on random walks provides many tools for computing properties such as steady-state probabilities or expected hitting times. Previously, however, there has been no g...
متن کاملEigenvalues of Random Power Law Graphs
Many graphs arising in various information networks exhibit the “power law” behavior – the number of vertices of degree k is proportional to k−β for some positive β. We show that if β > 2.5, the largest eigenvalue of a random power law graph is almost surely (1 + o(1)) √ m where m is the maximum degree. Moreover, the k largest eigenvalues of a random power law graph with exponent β have power l...
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ژورنال
عنوان ژورنال: Physical Review E
سال: 2006
ISSN: 1539-3755,1550-2376
DOI: 10.1103/physreve.74.051124