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

2019
*
arXiv
*
pre-print

For these processes,

arXiv:1805.07634v2
fatcat:pwzf77u5tbhbpjhdpc5vq2yfji
*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). ...##
###
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. ...

##
###
Harry Kesten's work in probability theory
[article]

2020
*
arXiv
*
pre-print

We survey

arXiv:2004.03861v2
fatcat:ysymucnkdrbt3mo4bntukjf76e
*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 ...##
###
Effect of scale on long-range random graphs and chromosomal inversions

2012
*
The Annals of Applied Probability
*

We show that

doi:10.1214/11-aap793
fatcat:6i7m7arzara5rp75zz4i5xsqky
*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*. ...##
###
Supercritical causal maps : geodesics and simple random walk
[article]

2019
*
arXiv
*
pre-print

We also study

arXiv:1806.10588v2
fatcat:u3jmzzfif5dfpiiul7j3a25gle
*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] . ...##
###
Classical localization and percolation in random environments on trees

1997
*
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
*

We consider

doi:10.1103/physreve.55.6765
fatcat:7gdmoc4e2zhkdmz26z5o7ttg5u
*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. ...##
###
Scaling limits of branching random walks and branching stable processes
[article]

2021
*
arXiv
*
pre-print

Here, we are interested

arXiv:2103.07404v2
fatcat:3wrn2a4tivbkfde7m6672nevda
*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. ...##
###
Positively and negatively excited random walks on integers, with branching processes
[article]

2008
*
arXiv
*
pre-print

We consider excited

arXiv:0801.1924v2
fatcat:52fw2zvtfbcv3cddmjrwo2js6u
*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*. ...##
###
Growth of Uniform Infinite Causal Triangulations

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. ...

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

2008
*
Electronic Journal of Probability
*

We consider excited

doi:10.1214/ejp.v13-572
fatcat:xcrbbmbrejb5lalmlrtrkeafau
*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*. ...##
###
A model of macroevolution with a natural system size
[article]

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 ...

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

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*. ...

##
###
Asymptotic Laws for Nonconservative Self-similar Fragmentations

2004
*
Electronic Journal of Probability
*

We show that under certain conditions

doi:10.1214/ejp.v9-215
fatcat:k2xlpxmkujbqzjt3esoeo3e5w4
*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] . ...##
###
DISPARITY: MORPHOLOGICAL PATTERN AND DEVELOPMENTAL CONTEXT

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. ...

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