16 citations · 49 across the 11 of their papers we have counts for
5 papers · 1 filter
Solution of the 15 puzzle problem
Yang Chu, Robert Hough
A generalized ` puzzle' consists of an numbered grid, with one missing number. A move in the game switches the position of the empty square with the position of on…
The spectrum of the abelian sandpile model
Robert Hough, Hyojeong Son
In their previous work, the authors studied the abelian sandpile model on graphs constructed from a growing piece of a plane or space tiling, given periodic or open boundary condit…
Cut-off for sandpiles on tiling graphs
Robert Hough, Hyojeong Son
Sandpile dynamics are considered on graphs constructed from periodic plane and space tilings by assigning a growing piece of the tiling either torus or open boundary conditions. A…
The local limit theorem on nilpotent Lie groups
Robert Hough
A local limit theorem is proven on connected, simply connected nilpotent Lie groups, for a class of generating measures satisfying a moment condition and a condition on the charact…
Sandpiles on the square lattice
Bob Hough, Dan Jerison, Lionel Levine
We give a non-trivial upper bound for the critical density when stabilizing i.i.d. distributed sandpiles on the lattice . We also determine the asymptotic spectral ga…