We present measurements of speckle in a random laser. We analyze its first-order statistics and show that, contrary to what might be expected for passive systems, analyses of the intensity distribution P(I) and the speckle spot size do provide information about light transport inside the system. P(I) is used to determine the degree to which an incident probe is amplified by the random laser. Th...

This paper presents a sampling-based method for path planning in robotic systems without known cost-to-go information. It uses trajectories generated from random search to heuristically learn the cost-to-go of regions within the configuration space. Gradually, the search is increasingly directed towards lower cost regions of the configuration space, thereby producing paths that converge towards...

The behaviour of a greedy algorithm which estimates the height of a random labelled rooted tree is studied. A self-similarity argument is used to characterize the limit distribution of the length H of the path found by such an algorithm in a random rooted tree as the unique solution of an integral equation. Furthermore, it is shown that lim n!1 E H p n = p 2 2 p 2 ln(3 + 2 p 2) = 2 : 353139::: ...

We consider anonymous communication protocols based on onions: each message is sent in an encrypted form through a path chosen at random by its sender, and the message is re-coded by each server on the path. Recently, it has been shown that if the anonymous paths are long enough, then the protocols provide provable security for some adversary models. However, it was assumed that all users choos...

This paper is concerned with finding a fingerprint of a sequence. As input data one uses the sequence which has been randomly mixed up by observing it along a random walk path. A sequence containing order exp(n) bits receives a fingerprint with roughly n bits information. The fingerprint is characteristic for the original sequence. With high probability the fingerprint depends only on the initi...

We consider first passage percolation on sparse random graphs with prescribed degree distributions and general independent and identically distributed edge weights assumed to have a density. Assuming that the degree distribution satisfies a uniform X logX-condition, we analyze the asymptotic distribution for the minimal weight path between a pair of typical vertices, as well the number of edges...

Analytic solution for the average path length in a large class of uncorrelated random networks with hidden variables is found. We apply the approach to classical random graphs of Erdös and Rényi (ER), evolving networks introduced by Barabási and Albert as well as random networks with asymptotic scale-free connectivity distributions characterized by an arbitrary scaling exponent α > 2. Our resul...

The path languages of random permitting context tree languages are investigated. The main result is that these path languages are regular. This confirms a previous conjecture. Copyright c © 2005 UMINF 05.23 ISSN 0348-0542

The harmonic explorer is a random grid path. Very roughly, at each step the harmonic explorer takes a turn to the right with probability equal to the discrete harmonic measure of the left hand side of the path from a point near the end of the current path. We prove that the harmonic explorer converges to SLE4 as the grid gets finer.