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The probabilities of extinction in a branching random walk on a strip [article]

Peter Braunsteins, Sophie Hautphenne
2019 arXiv   pre-print
For these processes, the probability q(A) of extinction in subsets of types A⊆X_d may differ from the global extinction probability q and the partial extinction probability q̃.  ...  Finally, we investigate the location of the vectors q(A) in the set of fixed points of the progeny generating vector.  ...  Acknowledgements The authors would like to acknowledge the support of the Australian Research Council (ARC) through the Centre of Excellence for the Mathematical and Statistical Frontiers (ACEMS).  ... 
arXiv:1805.07634v2 fatcat:pwzf77u5tbhbpjhdpc5vq2yfji

Page 6367 of Mathematical Reviews Vol. , Issue 2004h [page]

2004 Mathematical Reviews  
On components of a factorized representation for the sojourn time of semicontinuous random walks in a strip. (Russian. Russian summary) Sibirsk. Mat.  ...  The author obtains an explicit expression for the components in a factorized representation for the sojourn time of a semicontinuous random walk in a strip.  ... 

JPR volume 57 issue 3 Cover and Back matter

2020 Journal of Applied Probability  
The probabilities of extinction in a branching random walk on a strip 832 LU LI, QINYU WU AND TIANTIAN MAO.  ...  On the behavior of the failure rate and reversed failure rate in engineering systems 911 MERRITT R. LYON AND HOSAM M. MAHMOUD.  ... 
doi:10.1017/jpr.2020.79 fatcat:7pxz7wwydbdqhiuwa2qsjivrjm

Harry Kesten's work in probability theory [article]

Geoffrey R. Grimmett
2020 arXiv   pre-print
We survey the published work of Harry Kesten in probability theory, with emphasis on his contributions to random walks, branching processes, percolation, and related topics.  ...  A complete bibliography is included of his publications.  ...  Acknowledgements The author thanks Jean Bertoin, Rick Durrett, and Ross Maller for their helpful comments on this article, and he gratefully acknowledges the thoughtful and detailed report of an anonymous  ... 
arXiv:2004.03861v2 fatcat:ysymucnkdrbt3mo4bntukjf76e

Effect of scale on long-range random graphs and chromosomal inversions

Nathanaël Berestycki, Richard Pymar
2012 The Annals of Applied Probability  
We show that the resulting random graph gets a giant component when L≫( n)^2 (when the mean degree exceeds 1) but not when L≪ n. The proof uses comparisons to branching random walks.  ...  We also consider a related process of random transpositions of n particles on a circle, where transpositions only occur again if the spacing is at most L.  ...  Let θ denote the survival probability of the branching random walk.  ... 
doi:10.1214/11-aap793 fatcat:6i7m7arzara5rp75zz4i5xsqky

Supercritical causal maps : geodesics and simple random walk [article]

Thomas Budzinski
2019 arXiv   pre-print
We also study the simple random walk on these maps: we identify their Poisson boundary and, in the case where the underlying tree has no leaf, we prove that the random walk has positive speed.  ...  These are the hyperbolic analog of the maps studied by Curien, Hutchcroft and Nachmias in arXiv:1710.03137, and a natural model of random hyperbolic geometry.  ...  Acknowledgments: I thank Nicolas Curien for his comments on earlier versions of this work, Arvind Singh for explanations about renewal theory, and Itai Benjamini for providing the reference [7] .  ... 
arXiv:1806.10588v2 fatcat:u3jmzzfif5dfpiiul7j3a25gle

Classical localization and percolation in random environments on trees

Paul C. Bressloff, Vincent M. Dwyer, Michael J. Kearney
1997 Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics  
We consider a simple model of transport on a regular tree, whereby species evolve according to the drift-diffusion equation, and the drift velocity on each branch of the tree is a quenched random variable  ...  The inverse of the steady-state amplitude at the origin is expressed in terms of a random geometric series whose convergence or otherwise determines whether the system is localized or delocalized.  ...  C j . ͑3.33͒ Consider a random walk on ⌫ starting from the origin.  ... 
doi:10.1103/physreve.55.6765 fatcat:7gdmoc4e2zhkdmz26z5o7ttg5u

Scaling limits of branching random walks and branching stable processes [article]

Jean Bertoin, Hairuo Yang
2021 arXiv   pre-print
Here, we are interested in their domains of attraction and describe explicit conditions for a branching random walk to converge after a proper magnification to a branching-stable process.  ...  This contrasts with deep results that have been obtained during the last decade on the asymptotic behavior of branching random walks and which involve either shifting without rescaling, or demagnification  ...  as the weak limits of certain families of branching random walks in discrete time.  ... 
arXiv:2103.07404v2 fatcat:3wrn2a4tivbkfde7m6672nevda

Positively and negatively excited random walks on integers, with branching processes [article]

Elena Kosygina, Martin P.W. Zerner
2008 arXiv   pre-print
We consider excited random walks on the integers with a bounded number of i.i.d. cookies per site which may induce drifts both to the left and to the right.  ...  The proofs are based on results from the literature concerning branching processes with migration and make use of a certain renewal structure.  ...  Moreover, given a tree for a branching process that becomes extinct in finite time, we can reconstruct the right excursion of the random walk.  ... 
arXiv:0801.1924v2 fatcat:52fw2zvtfbcv3cddmjrwo2js6u

Growth of Uniform Infinite Causal Triangulations

V. Sisko, A. Yambartsev, S. Zohren
2013 Journal of statistical physics  
A relation to a random walk on the integer half line is shown.  ...  This relation is used to estimate the geodesic distance of a given triangle to the rooted boundary in terms of the time of the growth process and to determine from this the fractal dimension.  ...  Acknowledgments The authors would like to thank Richard Gill for fruitful discussions. The work of V.  ... 
doi:10.1007/s10955-012-0665-9 fatcat:r3eoy7sesrah3f3bhrqdu3nqbi

Positively and negatively excited random walks on integers, with branching processes

Elena Kosygina, Martin Zerner
2008 Electronic Journal of Probability  
We consider excited random walks on with a bounded number of i.i.d. cookies per site which may induce drifts both to the left and to the right.  ...  The proofs are based on results from the literature concerning branching processes with migration and make use of a certain renewal structure.  ...  Moreover, given a tree for a branching process that becomes extinct in finite time, we can reconstruct the right excursion of the random walk.  ... 
doi:10.1214/ejp.v13-572 fatcat:xcrbbmbrejb5lalmlrtrkeafau

A model of macroevolution with a natural system size [article]

D. A. Head, G. J. Rodgers
1998 arXiv   pre-print
A first principles approach is taken in which the probability for speciation and extinction are defined purely in terms of the fitness landscapes of each species.  ...  We describe a simple model of evolution which incorporates the branching and extinction of species lines, and also includes abiotic influences.  ...  Hence the rate of extinction will approach its upper bound value of k E ≈ K − 1 4 . (27) When a barrier is assigned a new value in the range [0,1], it undergoes an unbiased random walk until it is again  ... 
arXiv:adap-org/9611003v2 fatcat:kknddfj3ivdj5osvnok6fwci2y

A phase transition in the random transposition random walk [article]

Nathanael Berestycki, Rick Durrett (Cornell University)
2004 arXiv   pre-print
walk on the group of permutations on n elements.  ...  Our work is motivated by Bourque and Pevzner's (2002) simulation study of the effectiveness of the parsimony method in studying genome rearrangement, and leads to a surprising result about the random transposition  ...  If c > 1 the distribution of nongiant components in the random graph is given by progeny of a Poisson Galton Watson process with mean c on the event of its extinction.  ... 
arXiv:math/0403259v2 fatcat:4xhw6ybribeihmmmlr4iqb4hsq

Asymptotic Laws for Nonconservative Self-similar Fragmentations

Jean Bertoin, Alexander Gnedin
2004 Electronic Journal of Probability  
We show that under certain conditions the typical size in the ensemble is of the order t −1/α and that the empirical distribution of sizes converges to a random limit which we characterise in terms of  ...  We show that under certain conditions the typical size in the ensemble is of the order t −1/α and that the empirical distribution of sizes converges to a random limit which we characterise in terms of  ...  The process Z(t) = {Z j (t)} with Z j (t) = − log X j (t) is then a continuoustime branching random walk, as studied in [36, 16] .  ... 
doi:10.1214/ejp.v9-215 fatcat:k2xlpxmkujbqzjt3esoeo3e5w4

DISPARITY: MORPHOLOGICAL PATTERN AND DEVELOPMENTAL CONTEXT

DOUGLAS H. ERWIN
2007 Palaeontology  
of a more homogeneous distribution of morphologies.  ...  in evolutionary radiations, and have emphasized the difference between taxonomic measures of morphological diversity and quantitative assessments of disparity.  ...  I have greatly appreciated perceptive and useful comments on an earlier draft of the manuscript from Michael Foote, Kevin Peterson and Phil Donoghue.  ... 
doi:10.1111/j.1475-4983.2006.00614.x fatcat:4wvcqj7c4vbvrhv2x6qba3dcl4
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