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Distributed Random Walks
[article]
2013
arXiv
pre-print
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The main contribution of this paper is a fast distributed algorithm for performing random walks. ...
We present a sublinear time distributed algorithm for performing random walks whose time complexity is sublinear in the length of the walk. ...
Applications Our faster distributed random walk algorithm can be used in speeding up distributed applications where random walks arise as a subroutine. ...
arXiv:1302.4544v1
fatcat:itx2hwxdtbcwdo5m2rao4tdyxy
Distributed Random Walks
2013
Journal of the ACM
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The main contribution of this paper is a fast distributed algorithm for performing random walks. ...
Our random walk algorithms can be used to speed up distributed algorithms in applications that use random walks as a subroutine. We present two main applications. ...
Our Results A Fast Distributed Random Walk Algorithm. ...
doi:10.1145/2432622.2432624
fatcat:xcknscu7fndvjo5irfc4tca3ei
Fast distributed random walks
2009
Proceedings of the 28th ACM symposium on Principles of distributed computing - PODC '09
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The main contribution of this paper is a fast distributed algorithm for performing random walks. ...
In this paper, we focus on the problem of performing random walks efficiently in a distributed network. ...
Is there a faster way to perform a random walk distributively? In particular, we consider the following basic random walk problem. Computing One Random Walk where Destination Outputs Source. ...
doi:10.1145/1582716.1582745
dblp:conf/podc/SarmaNP09
fatcat:cmupbihr6ze4fh4wzyjtqmh5qe
Reinforced random walks and random distributions
1990
Proceedings of the American Mathematical Society
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It is shown that the empirical distribution {i < n: Zi < s}fn converges weakly and the distribution of this limit is the same as a standard Dubins-Freedman random distribution. ...
This process generates an exchangeable sequence of random variables Zn , with values in [0,1]. ...
*=o Thus, the variance of the expected value of a P-random distribution is 1/40. □
exchangeable sequence of random variables. ...
doi:10.1090/s0002-9939-1990-1012934-1
fatcat:oc66ks6v3veqxabeu7tgaxvfzu
Reinforced Random Walks and Random Distributions
1990
Proceedings of the American Mathematical Society
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It is shown that the empirical distribution {i < n: Zi < s}fn converges weakly and the distribution of this limit is the same as a standard Dubins-Freedman random distribution. ...
This process generates an exchangeable sequence of random variables Zn , with values in [0,1]. ...
*=o Thus, the variance of the expected value of a P-random distribution is 1/40. □
exchangeable sequence of random variables. ...
doi:10.2307/2048266
fatcat:pyqlvb4hx5buvh4qhhoq2h62vq
Random-walk in Beta-distributed random environment
2016
Probability theory and related fields
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2015 pre-print arXiv:1503.04117v2 fatcat:z3edhgippjd7bp26lflypel5raOther Versions
This is a random walk in ℤ which performs nearest neighbour jumps with transition probabilities drawn according to the Beta distribution. ...
We introduce an exactly-solvable model of random walk in random environment that we call the Beta RWRE. ...
This path is distributed as a directed random walk. • At time t, from each point in the percolation cluster where a random walk can branch, we add to the percolation cluster after an exponentially distributed ...
doi:10.1007/s00440-016-0699-z
fatcat:zdy32i5ozjde7cqfrknevr2znq
On the overlap distribution of Branching Random Walks
2016
Electronic Journal of Probability
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2016 pre-print arXiv:1509.07527v3 fatcat:aqiufcfrxbhtzgn3bgnbshpc4uOther Versions
In this paper, we study the overlap distribution and Gibbs measure of the Branching Random Walk with Gaussian increments on a binary tree. ...
The main technical result is a proof that the overlap distribution for the Branching Random Walk is supported on the set {0,1}. ...
We define the Branching Random Walk by H(v) = β∈p(v) g β where p(v) is the root leaf path to v excluding the root. ...
doi:10.1214/16-ejp3
fatcat:q425p3rvgfc5fbbuu74pumay2y
Random walk on nonnegative integers in beta distributed random environment
[article]
2022
arXiv
pre-print
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the same as for the analogous random walk on ℤ. ...
We consider random walks on the nonnegative integers in a space-time dependent random environment. ...
The marginal distribution of each random walk is the half-space beta RWRE. ...
arXiv:2201.07270v2
fatcat:rtoeasevojbudhibvijjsradfu
Efficient Distributed Random Walks with Applications
[article]
2010
arXiv
pre-print
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We focus on the problem of performing random walks efficiently in a distributed network. ...
Our random walk algorithms are useful in speeding up distributed algorithms for a variety of applications that use random walks as a subroutine. We present two main applications. ...
class of distributed random walk algorithms. ...
arXiv:0911.3195v2
fatcat:mn4ssqxoazg2dayzgcgr6f5jku
Weak quenched limiting distributions for transient one-dimensional random walk in a random environment
[article]
2016
arXiv
pre-print
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When 0<κ<2, the averaged distributions of the hitting times of the random walk converge to a κ-stable distribution. ...
We consider a one-dimensional, transient random walk in a random i.i.d. environment. ...
It was not until more recently that the limiting distributions of the hitting time and the random walk were studied under the quenched distribution. ...
arXiv:1011.6366v4
fatcat:6uhvuc7375a2zp3x6tdyucm3xi
Probability distribution of constrained Random Walks
[article]
2014
arXiv
pre-print
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In particular, their distribution is not i.i.d. We compute the limiting distribution of this sequence using the method of images. ...
Can this idea of "method of images" be used to find the limiting distribution of constrained random walks defined on a free group (or a finitely generated group)? ...
Introduction We study the following question -suppose a particle is taking a random walk on a finite rod. What is the chance that it will be at a particular position? ...
arXiv:1412.3902v1
fatcat:hklp7m7bafdlxeycksmsre5agi
Translation-Randomizable Distributions via Random Walks
[chapter]
2013
Lecture Notes in Computer Science
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Using a novel approach based on random walks, we construct families of such distributions, which are translation-randomizable over infinite groups. ...
a long (super-polynomial length) walk. ...
Here,μ k is a distribution on the free group coming from random walks of length bounded below by k. ...
doi:10.1007/978-3-642-41227-1_15
fatcat:uy73jype3nfjvg236wyg4e5qk4
Efficient distributed random walks with applications
2010
Proceeding of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing - PODC '10
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We focus on the problem of performing random walks efficiently in a distributed network. ...
We first present a fast sublinear time distributed algorithm for performing random walks whose time complexity is sublinear in the length of the walk. ...
class of distributed random walk algorithms. ...
doi:10.1145/1835698.1835745
dblp:conf/podc/SarmaNPT10
fatcat:v5pn2ebkivdhtitflo5x5q4qny
Matrix geometric approach for random walks: stability condition and equilibrium distribution
[article]
2017
arXiv
pre-print
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Furthermore, we consider the sub-class of random walks with equilibrium distributions given as series of product-forms and, for this class of random walks, we calculate the eigenvalues and the corresponding ...
In this paper, we analyse a sub-class of two-dimensional homogeneous nearest neighbour (simple) random walk restricted on the lattice using the matrix geometric approach. ...
Conclusions and future work In this paper, we generalise the QBD drift conditions for random walks in the lattice and illustrate the connection between the form of the equilibrium distribution depicted ...
arXiv:1603.04842v4
fatcat:sal54ywcurfozfla4stpkxebgi
Almost invariance of distributions for random walks on groups
[article]
2016
arXiv
pre-print
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We prove that simple random walks on wreath products of Z with finite groups have almost invariant distributions. ...
L(n) denotes the drift function of the random walk. ...
Then the distributions of the random walk pG, µq are almost invariant on the scale rpnq if rpnq{ ? n Ñ 0. Proof. ...
arXiv:1603.01458v2
fatcat:iggtskc42bgcnd37n3ot6cflg4
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