An isoperimetrlc inequality for random quadrangle tessellations

摘要

Random tessellations in the Euclidean plane are considered which are formed by random quadrangles. Every vertex is supposed to be incident with four edges. The following isoperimetric problem is solved under the assumption that the random tessel#xAC;lations are stationary and ergodic: The minimum value of the density of edge lengths is determined in the class of random quadrangle tesselations with given mean area of cells