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Biased random walks

1996
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Combinatorica
*

How much can an imperfect source of

doi:10.1007/bf01300124
fatcat:sp3dnws4hba4vnnjz2t7hot6vq
*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. ...##
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Biased random walks

1992
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Proceedings of the twenty-fourth annual ACM symposium on Theory of computing - STOC '92
*

How much can an imperfect source of

doi:10.1145/129712.129713
dblp:conf/stoc/AzarBKLP92
fatcat:xbw4a55uybhnnno3n4rgdya2ci
*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. ...##
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Biased random walks on random combs

2007
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Journal of Physics A: Mathematical and Theoretical
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We develop rigorous, analytic techniques to study the behaviour of

doi:10.1088/1751-8113/40/29/005
fatcat:dinysviglretxk4mmybrrcvnbi
*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. ...##
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Biased random walks on random graphs
[article]

2014
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arXiv
*
pre-print

The aim is to review recent mathematical developments in the field of

arXiv:1406.5076v1
fatcat:v2u35iy5ijaxlg4xh67ssgh2d4
*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 . ...##
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Biased random walk on the trace of biased random walk on the trace of..
[article]

2019
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arXiv
*
pre-print

We study the behaviour of a sequence of

arXiv:1901.04673v1
fatcat:hlqlupn2drdafjuslk2dgyxt3u
*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] . ...##
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Time Dependent Biased Random Walks
[article]

2021
*
arXiv
*
pre-print

We study the

arXiv:2006.02475v2
fatcat:q2b4f3bb3rd4vds2tx7kx3odma
*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. ...##
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Absorbing-state phase transition in biased activated random walk
[article]

2017
*
arXiv
*
pre-print

We consider the activated

arXiv:1403.1986v5
fatcat:6oufksrharf3zgxl2tnrezsska
*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. ...##
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An introduction to the trapping experienced by biased random walk on the trace of biased random walk
[article]

2020
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arXiv
*
pre-print

We introduce and summarise results from the recent paper '

arXiv:2003.06950v1
fatcat:vgmhwep6fna7bellbqueqycbde
*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. ...##
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Localization Transition of Biased Random Walks on Random Networks

2007
*
Physical Review Letters
*

We study

doi:10.1103/physrevlett.99.098701
pmid:17931043
fatcat:z2r5f724prgcjcg2asjgpgxnuq
*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. ...##
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Regularity of biased 1D random walks in random environment
[article]

2018
*
arXiv
*
pre-print

We study the asymptotic properties of nearest-neighbor

arXiv:1802.07874v2
fatcat:ociv54dzu5hepaw6lduibyubre
*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. ...##
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Biased random walk on the interlacement set
[article]

2017
*
arXiv
*
pre-print

We study a

arXiv:1610.02979v2
fatcat:yo66ipuk5vg7fnezsu6h2sxs3y
*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] ). ...##
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The speed of biased random walk on percolation clusters
[article]

2003
*
arXiv
*
pre-print

We consider

arXiv:math/0211303v3
fatcat:utc76sxspfgwpayy7vzgpcpytm
*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 . ...##
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Biased random walks and propagation failure

2007
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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

doi:10.1103/physreve.75.011118
pmid:17358121
fatcat:ypxo4x5yxrfddgs4annthpzvja
*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. ...##
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Fragment formation in biased random walks

2008
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Journal of Statistical Mechanics: Theory and Experiment
*

We analyse a

doi:10.1088/1742-5468/2008/10/p10002
fatcat:6skdahlz2nhtded62g6bemuqje
*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] . ...##
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Core-biased random walks in networks

2018
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Journal of Complex Networks
*

We present some examples based on real and artificial networks showing that the core-

doi:10.1093/comnet/cny001
fatcat:cet6blm4bvb7fngk6kqi76377i
*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*. ...
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