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Distributed Random Walks [article]

Atish Das Sarma, Danupon Nanongkai, Gopal Pandurangan, Prasad Tetali
2013 arXiv   pre-print
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

Atish Das Sarma, Danupon Nanongkai, Gopal Pandurangan, Prasad Tetali
2013 Journal of the ACM  
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

Atish Das Sarma, Danupon Nanongkai, Gopal Pandurangan
2009 Proceedings of the 28th ACM symposium on Principles of distributed computing - PODC '09  
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

R. Daniel Mauldin, S. C. Williams
1990 Proceedings of the American Mathematical Society  
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

R. Daniel Mauldin, S. C. Williams
1990 Proceedings of the American Mathematical Society  
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

Guillaume Barraquand, Ivan Corwin
2016 Probability theory and related fields  
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

Aukosh Jagannath
2016 Electronic Journal of Probability  
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]

Guillaume Barraquand, Mark Rychnovsky
2022 arXiv   pre-print
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]

Atish Das Sarma, Danupon Nanongkai, Gopal Pandurangan, Prasad Tetali
2010 arXiv   pre-print
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]

Jonathon Peterson, Gennady Samorodnitsky
2016 arXiv   pre-print
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]

Ritwik Mukherjee
2014 arXiv   pre-print
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]

Nirattaya Khamsemanan, William E. Skeith
2013 Lecture Notes in Computer Science  
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

Atish Das Sarma, Danupon Nanongkai, Gopal Pandurangan, Prasad Tetali
2010 Proceeding of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing - PODC '10  
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]

Stella Kapodistria, Zbigniew Palmowski
2017 arXiv   pre-print
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]

Anna Erschler
2016 arXiv   pre-print
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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