291 citations · 426 across the 19 of their papers we have counts for
10 papers · 1 filter
Hidden Ancestor Graphs: Models for Detagging Property Graphs
R. W. R. Darling, Gregory S. Clark, J. D. Tucker
Consider a graph where each vertex is visibly labelled as a member of a distinct class, but also has a hidden binary state: wild or tame. Edges with end points in the same clas…
Euclidean Embedding of the Poisson Weighted Infinite Tree and Application to Mobility Models
R. W. R. Darling, Robin Pemantle
Continuous time branching models are used to create random fractals in a Euclidean space, whose Hausdorff dimension is controlled by an input parameter. Finite realizations are app…
Rank deficiency in sparse random GF[2] matrices
R. W. R. Darling, Mathew D. Penrose, Andrew R. Wade +1
Let be a random matrix with binary entries and i.i.d. rows. The weight (i.e., number of ones) of a row has a specified probability distribution, with the row chose…
Differential equation approximations for Markov chains
R. W. R. Darling, J. R. Norris
We formulate some simple conditions under which a Markov chain may be approximated by the solution to a differential equation, with quantifiable error probabilities. The role of a…
Structure of large random hypergraphs
R. W. R. Darling, J. R. Norris
The theme of this paper is the derivation of analytic formulae for certain large combinatorial structures. The formulae are obtained via fluid limits of pure jump-type Markov proce…
Fluid Limits of Pure Jump Markov Processes: a Practical Guide
R. W. R. Darling
A rescaled Markov chain converges uniformly in probability to the solution of an ordinary differential equation, under carefully specified assumptions. The presentation is much sim…