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Distributed Random Walks
[article]

2013
*
arXiv
*
pre-print

The main contribution of this paper is a fast

arXiv:1302.4544v1
fatcat:itx2hwxdtbcwdo5m2rao4tdyxy
*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. ...##
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Distributed Random Walks

2013
*
Journal of the ACM
*

The main contribution of this paper is a fast

doi:10.1145/2432622.2432624
fatcat:xcknscu7fndvjo5irfc4tca3ei
*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. ...##
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Fast distributed random walks

2009
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Proceedings of the 28th ACM symposium on Principles of distributed computing - PODC '09
*

The main contribution of this paper is a fast

doi:10.1145/1582716.1582745
dblp:conf/podc/SarmaNP09
fatcat:cmupbihr6ze4fh4wzyjtqmh5qe
*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. ...##
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Reinforced random walks and random distributions

1990
*
Proceedings of the American Mathematical Society
*

It is shown that the empirical

doi:10.1090/s0002-9939-1990-1012934-1
fatcat:oc66ks6v3veqxabeu7tgaxvfzu
*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. ...##
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Reinforced Random Walks and Random Distributions

1990
*
Proceedings of the American Mathematical Society
*

It is shown that the empirical

doi:10.2307/2048266
fatcat:pyqlvb4hx5buvh4qhhoq2h62vq
*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. ...##
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Random-walk in Beta-distributed random environment

2016
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Probability theory and related fields
*

This is a

doi:10.1007/s00440-016-0699-z
fatcat:zdy32i5ozjde7cqfrknevr2znq
*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*...##
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On the overlap distribution of Branching Random Walks

2016
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Electronic Journal of Probability
*

In this paper, we study the overlap

doi:10.1214/16-ejp3
fatcat:q425p3rvgfc5fbbuu74pumay2y
*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. ...##
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Random walk on nonnegative integers in beta distributed random environment
[article]

2022
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arXiv
*
pre-print

the same as for the analogous

arXiv:2201.07270v2
fatcat:rtoeasevojbudhibvijjsradfu
*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. ...##
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Efficient Distributed Random Walks with Applications
[article]

2010
*
arXiv
*
pre-print

We focus on the problem of performing

arXiv:0911.3195v2
fatcat:mn4ssqxoazg2dayzgcgr6f5jku
*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. ...##
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Weak quenched limiting distributions for transient one-dimensional random walk in a random environment
[article]

2016
*
arXiv
*
pre-print

When 0<κ<2, the averaged

arXiv:1011.6366v4
fatcat:6uhvuc7375a2zp3x6tdyucm3xi
*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*. ...##
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Probability distribution of constrained Random Walks
[article]

2014
*
arXiv
*
pre-print

In particular, their

arXiv:1412.3902v1
fatcat:hklp7m7bafdlxeycksmsre5agi
*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? ...##
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Translation-Randomizable Distributions via Random Walks
[chapter]

2013
*
Lecture Notes in Computer Science
*

Using a novel approach based on

doi:10.1007/978-3-642-41227-1_15
fatcat:uy73jype3nfjvg236wyg4e5qk4
*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. ...##
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Efficient distributed random walks with applications

2010
*
Proceeding of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing - PODC '10
*

We focus on the problem of performing

doi:10.1145/1835698.1835745
dblp:conf/podc/SarmaNPT10
fatcat:v5pn2ebkivdhtitflo5x5q4qny
*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. ...##
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Matrix geometric approach for random walks: stability condition and equilibrium distribution
[article]

2017
*
arXiv
*
pre-print

Furthermore, we consider the sub-class of

arXiv:1603.04842v4
fatcat:sal54ywcurfozfla4stpkxebgi
*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 ...##
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Almost invariance of distributions for random walks on groups
[article]

2016
*
arXiv
*
pre-print

We prove that simple

arXiv:1603.01458v2
fatcat:iggtskc42bgcnd37n3ot6cflg4
*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. ...
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