The scaling limit of random simple triangulations and random simple quadrangulations

The Scaling Limit of Random Simple Triangulations and Random Simple Quadrangulations

The scaling limit of random simple triangulations and random simple quadrangulations . . . . . . . . . . . . . LOUIGI ADDARIO-BERRY AND MARIE ALBENQUE 2767 Recurrence and transience for the frog model on trees CHRISTOPHER HOFFMAN, TOBIAS JOHNSON AND MATTHEW JUNGE 2826 Stochastic De Giorgi iteration and regularity of stochastic partial differential equations ELTON P. HSU, YU WANG AND ZHENAN WANG...

The Scaling Limit of Random Simple Triangulations and Random Simple Quadrangulations

Let Mn be a simple triangulation of the sphere S, drawn uniformly at random from all such triangulations with n vertices. Endow Mn with the uniform probability measure on its vertices. After rescaling graph distance by (3/(4n)), the resulting random measured metric space converges in distribution, in the Gromov–Hausdorff– Prokhorov sense, to the Brownian map. In proving the preceding fact, we i...

Scaling Limit of Random Planar Quadrangulations with a Boundary

We discuss the scaling limit of large planar quadrangulations with a boundary whose length is of order the square root of the number of faces. We consider a sequence (σn) of integers such that σn/ √ 2n tends to some σ ∈ [0,∞]. For every n ≥ 1, we call qn a random map uniformly distributed over the set of all rooted planar quadrangulations with a boundary having n faces and 2σn half-edges on the...

Scaling limit of simple random walk on supercritical percolation clusters

The splitting design that leads to simple random sampling

Implementing unequal probability sampling, without replacement, is very complex and several methods have been suggested for its performance, including : Midseno design and systematic design. One of the methods that have been introduced by Devil and Tille (1998) is the splitting design that leads to simple random sampling .in this paper by completely explaining the design, with an example, we ha...