Filters








114,431 Hits in 3.8 sec

Biased random walks

Yossi Azar, Andrei Z. Broder, Anna R. Karlin, Nathan Linial, Steven Phillips
1996 Combinatorica  
How much can an imperfect source of randomness a ect an algorithm? We examine several simple questions of this type concerning the long-term behavior of a random walk on a nite graph.  ...  In our setup, at each step of the random walk a \controller" can, with a certain small probability, x the next step, thus introducing a bias.  ...  We use the relationship between biased random walk strategies and Markov decision theory 9] in order to show that there is a time-independent optimal strategy.  ... 
doi:10.1007/bf01300124 fatcat:sp3dnws4hba4vnnjz2t7hot6vq

Biased random walks

Yossi Azar, Andrei Z. Broder, Anna R. Karlin, Nathan Linial, Steven Phillips
1992 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing - STOC '92  
How much can an imperfect source of randomness a ect an algorithm? We examine several simple questions of this type concerning the long-term behavior of a random walk on a nite graph.  ...  In our setup, at each step of the random walk a \controller" can, with a certain small probability, x the next step, thus introducing a bias.  ...  We use the relationship between biased random walk strategies and Markov decision theory 9] in order to show that there is a time-independent optimal strategy.  ... 
doi:10.1145/129712.129713 dblp:conf/stoc/AzarBKLP92 fatcat:xbw4a55uybhnnno3n4rgdya2ci

Biased random walks on random combs

Tanya M Elliott, John F Wheater
2007 Journal of Physics A: Mathematical and Theoretical  
We develop rigorous, analytic techniques to study the behaviour of biased random walks on combs.  ...  Two specific examples of random comb ensembles are discussed; the random comb with nonzero probability of an infinitely long tooth at each vertex on the spine and the random comb with a power law distribution  ...  Biased random walks We regard time as integer valued and consider a walker who makes one step on the graph for each unit time interval.  ... 
doi:10.1088/1751-8113/40/29/005 fatcat:dinysviglretxk4mmybrrcvnbi

Biased random walks on random graphs [article]

Gerard Ben Arous, Alexander Fribergh
2014 arXiv   pre-print
The aim is to review recent mathematical developments in the field of random walks in random environment.  ...  Our main focus will be on directionally transient and reversible random walks on different types of underlying graph structures, such as Z, trees and Z^d for d≥ 2.  ...  In particular the β 2 -biased random walk is faster than the β 1 -biased random walk on T b .  ... 
arXiv:1406.5076v1 fatcat:v2u35iy5ijaxlg4xh67ssgh2d4

Biased random walk on the trace of biased random walk on the trace of.. [article]

David Croydon, Mark Holmes
2019 arXiv   pre-print
We study the behaviour of a sequence of biased random walks X(i), i>=0 on a sequence of random graphs, where the initial graph is Zd and otherwise the graph for the i-th walk is the trace of the (i - 1  ...  )-st walk.  ...  Finally, we note that, in another related work, biased random walk on an unbiased random walk has been shown to exhibit localisation on a logarithmic scale [8] .  ... 
arXiv:1901.04673v1 fatcat:hlqlupn2drdafjuslk2dgyxt3u

Time Dependent Biased Random Walks [article]

John Haslegrave, Thomas Sauerwald, John Sylvester
2021 arXiv   pre-print
We study the biased random walk where at each step of a random walk a "controller" can, with a certain small probability, move the walk to an arbitrary neighbour.  ...  [STOC'1992]; we extend their work to the time dependent setting and consider cover times of this walk. We obtain new bounds on the cover and hitting times.  ...  Preliminaries We shall now formally describe the ε-biased and ε-time-biased random walk model and introduce some notation.  ... 
arXiv:2006.02475v2 fatcat:q2b4f3bb3rd4vds2tx7kx3odma

Absorbing-state phase transition in biased activated random walk [article]

Lorenzo Taggi
2017 arXiv   pre-print
We consider the activated random walk (ARW) model on Z^d, which undergoes a transition from an absorbing regime to a regime of sustained activity.  ...  This answers a question from Rolla and Sidoravicius (2012) and Dickman, Rolla and Sidoravicius (2010) in the case of biased jump distribution.  ...  As the random walk is biased to the right, we can uniformly bound from below by a constant F L the probability of a successful jump.  ... 
arXiv:1403.1986v5 fatcat:6oufksrharf3zgxl2tnrezsska

An introduction to the trapping experienced by biased random walk on the trace of biased random walk [article]

David A. Croydon
2020 arXiv   pre-print
We introduce and summarise results from the recent paper 'Biased random walk on the trace of biased random walk on the trace of ...', which was written jointly with M. P.  ...  Biased random walk on the trace of biased random walk We now come to the main focus of this article -the biased random walk on the trace of biased random walk (BRWBRW).  ...  Conditional on G (0) , we then let X (1) be the β-biased random walk on this graph, defined similarly to the biased random walk on a percolation cluster.  ... 
arXiv:2003.06950v1 fatcat:vgmhwep6fna7bellbqueqycbde

Localization Transition of Biased Random Walks on Random Networks

Vishal Sood, Peter Grassberger
2007 Physical Review Letters  
We study random walks on large random graphs that are biased towards a randomly chosen but fixed target node.  ...  By extending rigorous results for biased walks on Galton-Watson trees, we give the exact analytical value for b_c and verify it by large scale simulations.  ...  We study random walks on large random graphs that are biased towards a randomly chosen but fixed target node.  ... 
doi:10.1103/physrevlett.99.098701 pmid:17931043 fatcat:z2r5f724prgcjcg2asjgpgxnuq

Regularity of biased 1D random walks in random environment [article]

Alessandra Faggionato, Michele Salvi
2018 arXiv   pre-print
We study the asymptotic properties of nearest-neighbor random walks in 1d random environment under the influence of an external field of intensity λ∈R.  ...  For the random conductance model we show that, in contrast with the deterministic case, σ^2(λ) is not monotone on the positive (resp. negative) half-line and that it is not differentiable at λ=0.  ...  The random walk X ω,λ n represents the biased discrete time RCM.  ... 
arXiv:1802.07874v2 fatcat:ociv54dzu5hepaw6lduibyubre

Biased random walk on the interlacement set [article]

Alexander Fribergh, Serguei Popov
2017 arXiv   pre-print
We study a biased random walk on the interlacement set of Z^d for d≥ 3.  ...  Although the walk is always transient, we can show, in the case d=3, that for any value of the bias the walk has a zero limiting speed and actually moves slower than any power.  ...  that if β is close enough to 1, then the biased random walk should have positive speed just as in the case of the biased random walk on percolation clusters (see [8] ).  ... 
arXiv:1610.02979v2 fatcat:yo66ipuk5vg7fnezsu6h2sxs3y

The speed of biased random walk on percolation clusters [article]

Noam Berger, Nina Gantert, Yuval Peres
2003 arXiv   pre-print
We consider biased random walk on supercritical percolation clusters in ^2.  ...  We show that the random walk is transient and that there are two speed regimes: If the bias is large enough, the random walk has speed zero, while if the bias is small enough, the speed of the random walk  ...  The biased random walk on the percolation cluster is a random walk in a random environment on Z 2 .  ... 
arXiv:math/0211303v3 fatcat:utc76sxspfgwpayy7vzgpcpytm

Biased random walks and propagation failure

Vicenç Méndez, Sergei Fedotov, Daniel Campos, Werner Horsthemke
2007 Physical Review E  
The critical value of the reaction rate able to sustain the propagation of an invasive front is obtained for general non-Markovian biased random walks with reactions.  ...  Arguably, the simplest random walk is Brownian motion. The random walk is biased if jumps in one particular direction are more likely and a drift in that direction will be observed ͓2͔.  ...  In summary, we have employed reaction-continuous-time random walks as a mesoscopic framework to study the opposing effects of biased random walks and logistic reactions on front propagation.  ... 
doi:10.1103/physreve.75.011118 pmid:17358121 fatcat:ypxo4x5yxrfddgs4annthpzvja

Fragment formation in biased random walks

Kabir Ramola
2008 Journal of Statistical Mechanics: Theory and Experiment  
We analyse a biased random walk on a 1D lattice with unequal step lengths.  ...  Such a walk was recently shown to undergo a phase transition from a state containing a single connected cluster of visited sites to one with several clusters of visited sites (fragments) separated by unvisited  ...  Introduction Anteneodo and Morgado recently discussed an interesting one-dimensional random walk model that exhibits a phase transition [1] .  ... 
doi:10.1088/1742-5468/2008/10/p10002 fatcat:6skdahlz2nhtded62g6bemuqje

Core-biased random walks in networks

Raúl J Mondragón
2018 Journal of Complex Networks  
We present some examples based on real and artificial networks showing that the core-biased random walk outperforms the degree-biased random walks. networks, entropy rate random walks, biased random walk  ...  It is known that biasing the random jump, the walker can explore every walk of the same length with equal probability, this is known as a Maximal Entropy Random Walk (MERW).  ...  We would justify the proposed biased random walk via a spectral bound of the adjacency matrix and show that this core-biased random walk can outperform the degree-biased random walk.  ... 
doi:10.1093/comnet/cny001 fatcat:cet6blm4bvb7fngk6kqi76377i
« Previous Showing results 1 — 15 out of 114,431 results