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

Massimiliano Ferrara

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.

Keywords


Stochastic Geometry, Probability, Integral Geometry, Exponential distribution.

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DOI: https://doi.org/10.1478/AAPP.1022A4

Copyright (c) 2024 Massimiliano Ferrara

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