Stochastic Geometry and Wireless Networks Volume I

Part I provides a compact survey on classical stochastic geometry models. The basic models defined
in this part will be used and extended throughout the whole monograph, and in particular to SINR based
models. Note however that these classical stochastic models can be used in a variety of contexts which
go far beyond the modeling of wireless networks. Chapter 1 reviews the definition and basic properties of
Poisson point processes in Euclidean space. We review key operations on Poisson point processes (thinning,
superposition, displacement) as well as key formulas like Campbell’s formula. Chapter 2 is focused on
properties of the spatial shot-noise process: its continuity properties, its Laplace transform, its moments
etc. Both additive and max shot-noise processes are studied. Chapter 3 bears on coverage processes,
and in particular on the Boolean model. Its basic coverage characteristics are reviewed. We also give a
brief account of its percolation properties. Chapter 4 studies random tessellations; the main focus is on
Poisson–Voronoi tessellations and cells. We also discuss various random objects associated with bivariate
point processes such as the set of points of the first point process that fall in a Voronoi cell w.r.t. the second
point process.

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