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Publications of Matthew S Junge    :chronological  alphabetical  combined listing:

%% Papers Published   
@article{fds340352,
   Author = {Brito, G and Fowler, C and Junge, M and Levy, A},
   Title = {Ewens Sampling and Invariable Generation},
   Journal = {Combinatorics, Probability and Computing},
   Volume = {27},
   Number = {6},
   Pages = {853-891},
   Publisher = {Cambridge University Press (CUP)},
   Year = {2018},
   Month = {November},
   url = {http://dx.doi.org/10.1017/S096354831800007X},
   Abstract = {© 2018 Cambridge University Press. We study the number of
             random permutations needed to invariably generate the
             symmetric group Sn when the distribution of cycle counts has
             the strong α-logarithmic property. The canonical example is
             the Ewens sampling formula, for which the special case α =
             1 corresponds to uniformly random permutations. For strong
             α-logarithmic measures and almost every α, we show that
             precisely [(1-αlog2)-1] permutations are needed to
             invariably generate Sn with asymptotically positive
             probability. A corollary is that for many other probability
             measures on Sn no fixed number of permutations will
             invariably generate Sn with positive probability. Along the
             way we generalize classic theorems of ErdÅ's, Tehran,
             Pyber, Łuczak and Bovey to permutations obtained from the
             Ewens sampling formula.},
   Doi = {10.1017/S096354831800007X},
   Key = {fds340352}
}

@article{fds335538,
   Author = {Johnson, T and Junge, M},
   Title = {Stochastic orders and the frog model},
   Journal = {Annales De L'Institut Henri Poincaré, Probabilités Et
             Statistiques},
   Volume = {54},
   Number = {2},
   Pages = {1013-1030},
   Publisher = {Institute of Mathematical Statistics},
   Year = {2018},
   Month = {May},
   url = {http://dx.doi.org/10.1214/17-aihp830},
   Doi = {10.1214/17-aihp830},
   Key = {fds335538}
}

@article{fds338420,
   Author = {Foxall, E and Hutchcroft, T and Junge, M},
   Title = {Coalescing random walk on unimodular graphs},
   Journal = {Electronic Communications in Probability},
   Volume = {23},
   Publisher = {Institute of Mathematical Statistics},
   Year = {2018},
   Month = {January},
   url = {http://dx.doi.org/10.1214/18-ECP136},
   Abstract = {© 2018, University of Washington. All rights reserved.
             Coalescing random walk on a unimodular random rooted graph
             for which the root has finite expected degree visits each
             site infinitely often almost surely. A corollary is that an
             opinion in the voter model on such graphs has infinite
             expected lifetime. Additionally, we deduce an adaptation of
             our main theorem that holds uniformly for coalescing random
             walk on finite random unimodular graphs with degree
             distribution stochastically dominated by a probability
             measure with finite mean.},
   Doi = {10.1214/18-ECP136},
   Key = {fds338420}
}

@article{fds339580,
   Author = {Beckman, E and Dinan, E and Durrett, R and Huo, R and Junge,
             M},
   Title = {Asymptotic behavior of the brownian frog
             model},
   Journal = {Electronic Journal of Probability},
   Volume = {23},
   Publisher = {Institute of Mathematical Statistics},
   Year = {2018},
   Month = {January},
   url = {http://dx.doi.org/10.1214/18-EJP215},
   Abstract = {© 2018, University of Washington. All rights reserved. We
             introduce an extension of the frog model to Euclidean space
             and prove properties for the spread of active particles. Fix
             r>0 and place a particle at each point x of a unit intensity
             Poisson point process P⊆ℝd−B(0,r). Around each point
             in P, put a ball of radius r. A particle at the origin
             performs Brownian motion. When it hits the ball around x for
             some x ∈ P, new particles begin independent Brownian
             motions from the centers of the balls in the cluster
             containing x. Subsequent visits to the cluster do nothing.
             This waking process continues indefinitely. For r smaller
             than the critical threshold of continuum percolation, we
             show that the set of activated points in P approximates a
             linearly expanding ball. Moreover, in any fixed ball the set
             of active particles converges to a unit intensity Poisson
             point process.},
   Doi = {10.1214/18-EJP215},
   Key = {fds339580}
}

@article{fds339742,
   Author = {Cristali, I and Ranjan, V and Steinberg, J and Beckman, E and Durrett,
             R and Junge, M and Nolen, J},
   Title = {Block size in geometric(P)-biased permutations},
   Journal = {Electronic Communications in Probability},
   Volume = {23},
   Publisher = {Institute of Mathematical Statistics},
   Year = {2018},
   Month = {January},
   url = {http://dx.doi.org/10.1214/18-ECP182},
   Abstract = {© 2018, University of Washington. All rights reserved. Fix
             a probability distribution p = (p1, p2, …) on the positive
             integers. The first block in a p-biased permutation can be
             visualized in terms of raindrops that land at each positive
             integer j with probability pj. It is the first point K so
             that all sites in [1, K] are wet and all sites in (K, ∞)
             are dry. For the geometric distribution pj = p(1 − p)j−1
             we show that p log K converges in probability to an explicit
             constant as p tends to 0. Additionally, we prove that if p
             has a stretch exponential distribution, then K is infinite
             with positive probability.},
   Doi = {10.1214/18-ECP182},
   Key = {fds339742}
}

@article{fds329100,
   Author = {Hoffman, C and Johnson, T and Junge, M},
   Title = {Recurrence and transience for the frog model on
             trees},
   Journal = {The Annals of Probability},
   Volume = {45},
   Number = {5},
   Pages = {2826-2854},
   Publisher = {Institute of Mathematical Statistics},
   Year = {2017},
   Month = {September},
   url = {http://dx.doi.org/10.1214/16-AOP1125},
   Abstract = {© Institute of Mathematical Statistics, 2017. The frog
             model is a growing system of random walks where a particle
             is added whenever a new site is visited. A longstanding open
             question is how often the root is visited on the infinite
             d-ary tree. We prove the model undergoes a phase transition,
             finding it recurrent for d = 2 and transient for d ≥ 5.
             Simulations suggest strong recurrence for d = 2, weak
             recurrence for d = 3, and transience for d ≥ 4.
             Additionally, we prove a 0-1 law for all d-ary trees, and we
             exhibit a graph on which a 0-1 law does not hold. To prove
             recurrence when d = 2, we construct a recursive
             distributional equation for the number of visits to the root
             in a smaller process and show the unique solution must be
             infinity a.s. The proof of transience when d = 5 relies on
             computer calculations for the transition probabilities of a
             large Markov chain. We also include the proof for d ≥ 6,
             which uses similar techniques but does not require computer
             assistance.},
   Doi = {10.1214/16-AOP1125},
   Key = {fds329100}
}

@article{fds325463,
   Author = {Hoffman, C and Johnson, T and Junge, M},
   Title = {From transience to recurrence with poisson tree
             frogs},
   Journal = {The Annals of Applied Probability},
   Volume = {26},
   Number = {3},
   Pages = {1620-1635},
   Publisher = {Institute of Mathematical Statistics},
   Year = {2016},
   Month = {June},
   url = {http://dx.doi.org/10.1214/15-AAP1127},
   Abstract = {© 2016 Institute of Mathematical Statistics. Consider the
             following interacting particle system on the d-ary tree,
             known as the frog model: Initially, one particle is awake at
             the root and i.i.d. Poisson many particles are sleeping at
             every other vertex. Particles that are awake perform simple
             random walks, awakening any sleeping particles they
             encounter. We prove that there is a phase transition between
             transience and recurrence as the initial density of
             particles increases, and we give the order of the transition
             up to a logarithmic factor.},
   Doi = {10.1214/15-AAP1127},
   Key = {fds325463}
}

@article{fds325464,
   Author = {Benjamini, I and Foxall, E and Gurel-Gurevich, O and Junge, M and Kesten, H},
   Title = {Site recurrence for coalescing random walk},
   Journal = {Electronic Communications in Probability},
   Volume = {21},
   Publisher = {Institute of Mathematical Statistics},
   Year = {2016},
   Month = {January},
   url = {http://dx.doi.org/10.1214/16-ECP5},
   Abstract = {© 2016, University of Washington. All rights reserved.
             Begin continuous time random walks from every vertex of a
             graph and have particles coalesce when they collide. We use
             a duality relation with the voter model to prove the process
             is site recurrent on bounded degree graphs, and for
             Galton-Watson trees whose offspring distribution has
             exponential tail. We prove bounds on the occupation
             probability of a site, as well as a general 0-1 law. Similar
             conclusions hold for a coalescing process on trees where
             particles do not backtrack.},
   Doi = {10.1214/16-ECP5},
   Key = {fds325464}
}

@article{fds325465,
   Author = {Johnson, T and Junge, M},
   Title = {The critical density for the frog model is the degree of the
             tree},
   Journal = {Electronic Communications in Probability},
   Volume = {21},
   Publisher = {Institute of Mathematical Statistics},
   Year = {2016},
   Month = {January},
   url = {http://dx.doi.org/10.1214/16-ECP29},
   Abstract = {© 2016, University of Washington. All rights reserved. The
             frog model on the rooted d-ary tree changes from transient
             to recurrent as the number of frogs per site is increased.
             We prove that the location of this transition is on the same
             order as the degree of the tree.},
   Doi = {10.1214/16-ECP29},
   Key = {fds325465}
}

@article{fds325466,
   Author = {Junge, M},
   Title = {Choices, intervals and equidistribution},
   Journal = {Electronic Journal of Probability},
   Volume = {20},
   Pages = {1-18},
   Publisher = {Institute of Mathematical Statistics},
   Year = {2015},
   Month = {September},
   url = {http://dx.doi.org/10.1214/EJP.v20-4191},
   Abstract = {© 2015, University of Washington. All right reserved. We
             give a sufficient condition for a random sequence in [0,1]
             generated by a Ψ process to be equidistributed. The
             condition is met by the canonical example – the max-2
             process – where the nth term is whichever of two uniformly
             placed points falls in the larger gap formed by the previous
             n — 1 points. This solves an open problem from Itai
             Benjamini, Pascal Maillard and Elliot Paquette. We also
             deduce equidistribution for more general Ψ-processes. This
             includes an interpolation of the min-2 and max-2 processes
             that is biased towards min-2.},
   Doi = {10.1214/EJP.v20-4191},
   Key = {fds325466}
}

 

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