A Laplace-type problem for a lattice with cell composed by regular polygons with obstacles

Abstract

In this paper we consider a lattice with a fundamental cell composed of two triangles and two trapezoids in the presence of some obstacles and we determine the probability p that a random segment with uniform and random distribution of constant length intersects a side of the lattice. By this note we solve a Stochastic Geometry’s open problem as well and we start to connect this field to some aspects related Artificial Intelligence issues.