5.7k citations · 8.2k across the 29 of their papers we have counts for
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Birth and death processes on certain random trees: Classification and stationary laws
Guy Fayolle, Maxim Krikun, Jean-Marc Lasgouttes
The main substance of the paper concerns the growth rate and the classification (ergodicity, transience) of a family of random trees. In the basic model, new edges appear according…
Phase transition for the Ising model on the Critical Lorentzian triangulation
Maxim Krikun, Anatoly Yambartsev
Ising model without external field on an infinite Lorentzian triangulation sampled from the uniform distribution is considered. We prove uniqueness of the Gibbs measure in the high…
On one property of distances in the infinite random quadrangulation
Maxim Krikun
We show that the Schaeffer's tree for an infinite quadrangulation only changes locally when changing the root of the quadrangulation. This follows from one property of distances in…
Connected allocation to Poisson points in R^2
Maxim Krikun
This note answers one question in [math.PR/0505668], concerning the connected allocation for the Poisson process in R^2. The proposed solution makes use of the Riemann map from the…
Local structure of random quadrangulations
Maxim Krikun
This paper is an adaptation of a method used in \cite{K} to the model of random quadrangulations. We prove local weak convergence of uniform measures on quadrangulations and show t…
Percolating paths through random points :
David Aldous, Maxim Krikun
We prove consistency of four different approaches to formalizing the idea of minimum average edge-length in a path linking some infinite subset of points of a Poisson process. The…