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Stochastic Geometry and Wireless Networks, Volume I: Thepory
, 2009
"... A wireless communication network can be viewed as a collection of nodes, located in some domain, which can in turn be transmitters or receivers (depending on the network considered, nodes may be mobile users, base stations in a cellular network, access points of a WiFi mesh etc.). At a given time, ..."
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Cited by 251 (35 self)
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given bit rate. The interference seen by a receiver is the sum of the signal powers received from all transmitters, except its own transmitter. Stochastic geometry provides a natural way of defining and computing macroscopic properties of such networks, by averaging over all potential geometrical
CLASSICAL STOCHASTIC GEOMETRY
"... The aim of this chapter is to introduce the basic tools and structures of stochastic geometry and thus to lay the foundations for much of the book. Before this, a brief historic account will reflect the development from elementary geometric probabilities over heuristic principles in applications to ..."
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Cited by 17 (1 self)
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The aim of this chapter is to introduce the basic tools and structures of stochastic geometry and thus to lay the foundations for much of the book. Before this, a brief historic account will reflect the development from elementary geometric probabilities over heuristic principles in applications
Perfect Simulation in Stochastic Geometry
"... Simulation plays an important role in stochastic geometry and related fields, because all but the simplest random set models tend to be intractable to analysis. Many simulation algorithms deliver (approximate) samples of such random set models, for example by simulating the equilibrium distribut ..."
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Cited by 34 (3 self)
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Simulation plays an important role in stochastic geometry and related fields, because all but the simplest random set models tend to be intractable to analysis. Many simulation algorithms deliver (approximate) samples of such random set models, for example by simulating the equilibrium
New Perspectives in Stochastic Geometry
 MATHEMATISCHES FORSCHUNGSINSTITUT OBERWOLFACH REPORT NO. 47/2008
, 2008
"... The workshop was devoted to the discussion and exploration of recent developments in stochastic geometry. Two main themes were new results and methodology in classical stochastic geometry and allocation and matching procedures for point processes and random measures. Mathematics Subject Classificat ..."
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Cited by 3 (0 self)
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The workshop was devoted to the discussion and exploration of recent developments in stochastic geometry. Two main themes were new results and methodology in classical stochastic geometry and allocation and matching procedures for point processes and random measures. Mathematics Subject
Stochastic Geometry and Random Tessellations
"... Random tessellations form a very important field in stochastic geometry. They pose many interesting mathematical problems and have numerous important applications in many branches of natural sciences and engineering, as this volume shows. This contribution aims to present mathematical basic facts as ..."
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Cited by 1 (0 self)
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Random tessellations form a very important field in stochastic geometry. They pose many interesting mathematical problems and have numerous important applications in many branches of natural sciences and engineering, as this volume shows. This contribution aims to present mathematical basic facts as
COMBINATORIAL FOUNDATIONS OF STOCHASTIC GEOMETRY
, 1978
"... Recently it has become clear that many results in stochastic geometry hinge on a single fundamental property, the solution to the socalled BujfonSylvester problem, which yields the classical 'integral geometric' identities in a more general form, as well as furnishing useful extra inform ..."
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Recently it has become clear that many results in stochastic geometry hinge on a single fundamental property, the solution to the socalled BujfonSylvester problem, which yields the classical 'integral geometric' identities in a more general form, as well as furnishing useful extra
Stochastic Geometry and Architecture of Communication Networks
 J. Telecommunication Systems
, 1995
"... This paper proposes a new approach for communication networks planning; this approach is based on stochastic geometry. We first summarize the state of the art in this domain, together with its economic implications, before sketching the main expectations of the proposed method. The main probabilisti ..."
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Cited by 84 (7 self)
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This paper proposes a new approach for communication networks planning; this approach is based on stochastic geometry. We first summarize the state of the art in this domain, together with its economic implications, before sketching the main expectations of the proposed method. The main
Stochastic Geometry Autumn 2004
, 2004
"... In stochastic geometry, mathematical models of random sets and random geometrical processes are developed and analyzed. The present course gives an introduction to the two main models of stochastic geometry: random sets and (ordinary) random point processes. Special emphasis is placed on a complete ..."
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In stochastic geometry, mathematical models of random sets and random geometrical processes are developed and analyzed. The present course gives an introduction to the two main models of stochastic geometry: random sets and (ordinary) random point processes. Special emphasis is placed on a complete
Stochastic Geometry and Statistical Mechanics
"... Stochastic geometry is an established field of mathematics that extends back into the nineteenth century at least, and arguably much earlier. Pioneers sometimes considered elementary problems in paradoxical ways, often deliberately. For example, in order to combat insomnia on the night of 20 January ..."
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Stochastic geometry is an established field of mathematics that extends back into the nineteenth century at least, and arguably much earlier. Pioneers sometimes considered elementary problems in paradoxical ways, often deliberately. For example, in order to combat insomnia on the night of 20
Size Distributions in Stochastic Geometry
, 1997
"... We indicate how granulometries may be useful in the analysis of random sets. We define a suitable size distribution function as a tool in exploratory data analysis and give a new Hanischstyle estimator for it. New Markov random sets are constructed which favour certain sizes above others. Applicati ..."
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distribution function. Note: Work carried out under project PNA4.4 "Stochastic geometry". 1. Introduction One of the most basic properties of an object is its size. It is no wonder then that size measures have been used for a long time in the empirical sciences, and more recently in the analysis
Results 1  10
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68,040