Random Walks III
ثبت نشده
چکیده
“ I gave the girl my protection, offering in my equivocal way to be her father. But I came too late, after she had ceased to believe in fathers. I wanted to do what was right, I wanted to make reparation: I will not deny this decent impulse, however mixed with more questionable motives: there must always be a place for penance and reparation. Nevertheless, I should never have allowed the gates of the town to be opened to people who assert that there are higher considerations that those of decency. They exposed her father to her naked and made him gibber with pain, they hurt her and he could not stop them (on a day I spent occupied with the ledgers in my office). Thereafter she was no longer fully human, sister to all of us. Certain sympathies died, certain movements of the heart became no longer possible to her. I too, if I live longer enough in this cell with its ghost not only of the father and the daughter but of the man who even by lamplight did not remove the black discs from his eyes and the subordinate whose work it was to keep the brazier fed, will be touched with the contagion and turned into a create that believes in nothing. ” – Waiting for the Barbarians, J. M. Coetzee.
منابع مشابه
A PRELUDE TO THE THEORY OF RANDOM WALKS IN RANDOM ENVIRONMENTS
A random walk on a lattice is one of the most fundamental models in probability theory. When the random walk is inhomogenous and its inhomogeniety comes from an ergodic stationary process, the walk is called a random walk in a random environment (RWRE). The basic questions such as the law of large numbers (LLN), the central limit theorem (CLT), and the large deviation principle (LDP) are ...
متن کاملThe cover time of a biased random walk on a random cubic graph
Our aim in this paper is to analyse a variation on a simple random walk that may tend to speed up the cover time of a connected graph. This variation is just one of several possible approaches which include (i) non-bactracking walks, see Alon, Benjamini, Lubetzky and Sodin [3], (ii) walks that prefer unused edges, see Berenbrink, Cooper and Friedetzky [4] or (iii) walks that a biassed toward lo...
متن کاملOn Dynamical Gaussian Random Walks
Motivated by the recent work of Benjamini, Häggström, Peres, and Steif (2003) on dynamical random walks, we: (i) Prove that, after a suitable normalization, the dynamical Gaussian walk converges weakly to the Ornstein–Uhlenbeck process in classical Wiener space; (ii) derive sharp tailasymptotics for the probabilities of large deviations of the said dynamical walk; and (iii) characterize (by way...
متن کاملLarge Deviations for Random Walks in a Mixing Random Environment and Other (Non-Markov) Random Walks
We extend a recent work by S. R. S. Varadhan [8] on large deviations for random walks in a product random environment to include more general random walks on the lattice. In particular, some reinforced random walks and several classes of random walks in Gibbs fields are included. c © 2004 Wiley Periodicals, Inc.
متن کاملReducing Search Lengths with Locally Precomputed Partial Random Walks
Random walks can be used to search complex networks for a desired resource. To reduce the number of hops necessary to find resources, we propose a search mechanism based on building random walks connecting together partial walks that have been precomputed at each network node in an initial stage. The resources found in each partial walk are registered in its associated Bloom filter. Searches ca...
متن کاملCOLORING A d ≥ 3 DIMENSIONAL LATTICE WITH TWO INDEPENDENT RANDOM WALKS
Without your support, I wouldn't be here. ii Acknowledgements Thanks to Robin Pemantle, for his mathematical guidance over the past three years and who, during the past year, has conveyed to me many of the ideas behind the results presented here. iii 1
متن کامل