Simply generated trees, conditioned Galton―Watson trees, random allocations and condensation: Extended abstract by Svante Janson

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The Height of List-tries and TST by N. Broutin, L. Devroye

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Processing and Transmission of Information by Hellman, M. E., Flower, R. A., Levitt, B. K., Kennedy, Robert S.

Subjects: “…Relationships between Random Trees and Branching Processes…”
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The Diameter of the Minimum Spanning Tree of a Complete Graph by Louigi Addario-Berry, Nicolas Broutin, Bruce Reed

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14.15J / 6.207J Networks, Fall 2009 by Acemoglu, Daron, Ozdaglar, Asu

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STRONG APPROXIMATIONS FOR EPIDEMIC MODELS by Ball, F, Donnelly, P

“…A construction of a sequence of such epidemics, indexed by the initial number of susceptibles N, from the limiting branching process is described. Strong convergence of the epidemic processes to the branching process is shown when the latter goes extinct. …”

The Hausdorff spectrum for a class of multifractal processes by Hambly, B, Decrouez, G, Jones, O

“…The Multifractal Embedded Branching Process (MEBP) process and Canonical Embedded Branching Process (CEBP) process were introduced by Decrouez and Jones (2012). …”

A note on weak convergence results for uniform infinite causal triangulations by Sisko, V, Yambartsev, A, Zohren, S

“…We discuss uniform infinite causal triangulations and equivalence to the size biased branching process measure - the critical Galton-Watson branching process distribution conditioned on non-extinction. …”

Approximating the epidemic curve by Barbour, A, Reinert, G

“…The numbers of infected individuals during the initial stages of an epidemic can be well approximated by a branching process, after which the proportion of individuals that are susceptible follows a more or less deterministic course. …”

A probabilistic model for interfaces in a martensitic phase transition by Cesana, P, Hambly, B

“…In doing so we extend a theorem on the growth of the general branching random walk as well as developing results on the tail behaviour of the limiting random variable in our general branching process. …”

Unambiguous and finitely ambiguous automata by Widdershoven, C

“…</p> <p>Lastly, we consider model checking of branching processes against LTL formulas using an automata theoretic approach. …”

The Asymptotic Behavior for Generalized Jiřina Process by You Lv, Huaping Huang

“…As the classic branching process, the Galton-Watson process has obtained intensive attentions in the past decades. …”
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From neuronal spikes to avalanches: Effects and circumvention of time binning by Johannes Pausch

“…First, the article introduces and characterizes a continuous-time version of the branching process with immigration, which will be called the pumped branching process, and second, it presents an analytical derivation of the corresponding spike statistics, which can be directly compared to observed spike time series. …”
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SuperBrownian motion and the spatial Lambda-Fleming-Viot process by Chetwynd-Diggle, J, Etheridge, A

“…It is well known that the dynamics of a subpopulation of individuals of a rare type in a Wright-Fisher diffusion can be approximated by a Feller branching process. Here we establish an analogue of that result for a spatially distributed population whose dynamics are described by a spatial Lambda-Fleming-Viot process (SLFV). …”

Will an outbreak exceed available resources for control? Estimating the risk from invading pathogens using practical definitions of a severe epidemic by Thompson, RN, Gilligan, CA, Cunniffe, NJ

“…Standard epidemic risk estimates involve assuming that infections occur according to a branching process and correspond to the probability that the outbreak persists beyond the initial stochastic phase. …”

On the geometric and analytic properties of some random fractals by Charmoy, P

“…</p> <p>To study the fluctuations around these asymptotics, we prove a central limit theorem for the general branching process. The proof follows a standard Taylor expansion argument and relies on the independence built into the general branching process. …”

The small giant component in scale-free random graphs by Riordan, O

“…In all cases the method used is to couple the neighbourhood expansion process in the graph on n vertices with a continuous-type branching process that is independent of n. It can be shown (requiring some separate argument for each case) that with probability tending to 1 as $n\to\infty$ the size of the giant component divided by n is within $o(1)$ of the survival probability $\ sigma$ of the branching process. …”

Textbook of Phylogenetics / by Krieger, Joshua, author 648873

“…Evolution is regarded as a branching process, whereby populations are altered over time and may speciate into separate branches, hybridize together, or terminate by extinction. …”
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Growth by basal branching in two species of Huicungo palms, Astrocaryum carnosum and A. huicungo by Miguel Machahua, Francis Kahn, Betty Millán

“…The basal branching process of Astrocaryum carnosum and A. huicungo is described and its rate and structural expression at the population level is analyzed. …”
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The shortest distance in random multi-type intersection graphs by Barbour, A, Reinert, G

“…Using an associated branching process as the basis of our approximation, we show that typical inter-point distances in a multitype random intersection graph have a defective distribution, which is well described by a mixture of translated and scaled Gumbel distributions, the missing mass corresponding to the event that the vertices are not in the same component of the graph.…”