| Description |
1 online resource (xiii, 330 pages) : illustrations |
| Series |
Oxford studies in probability ; 5 |
|
Oxford studies in probability ; 5.
|
| Contents |
Motivation and history -- Statistical background -- Computer science background -- Outline of results -- Some basic definitions -- Elements of probability -- Poissonization -- Probabilistic ingredients -- Dependency graphs and Poisson approximation -- Multivariate Poisson approximation -- Normal approximation -- Martingale theory -- De-Poissonization -- Subgraph and component counts -- Expectations -- Poisson approximation -- Second moments in a Poisson process -- Normal approximation for Poisson processes -- Normal approximation: de-Poissonization -- Strong laws of large numbers -- Typical vertex degrees -- The setup -- Laws of large numbers -- Asymptotic covariances -- Moments for de-Poissonization -- Finite-dimensional central limit theorems -- Convergence in Skorohod space -- Geometrical ingredients -- Consequences of the Lebesgue density theorem -- Covering, packing, and slicing -- The Brunn-Minkowski inequality -- Expanding sets in the orthant -- Maximum degree, cliques, and colourings -- Focusing -- Subconnective laws of large numbers -- More laws of large numbers for maximum degree -- Laws of large numbers for clique number -- The chromatic number -- Minimum degree: laws of large numbers -- Thresholds in smoothly bounded regions -- Strong laws for thresholds in the cube -- Strong laws for the minimum degree -- Minimum degree: convergence in distribution -- Uniformly distributed points I -- Uniformly distributed points II -- Normally distributed points I -- Normally distributed points II -- Percolative ingredients |
| Summary |
This monograph provides and explains the mathematics behind geometric graph theory, which studies the properties of a graph that consists of nodes placed in Euclidean space so that edges can be added to connect points that are close to one another |
| Bibliography |
Includes bibliographical references and index |
| Notes |
English |
| Subject |
Random graphs.
|
|
MATHEMATICS -- Graphic Methods.
|
|
Random graphs
|
|
Grafentheorie.
|
|
Combinatória.
|
| Form |
Electronic book
|
| ISBN |
0198506260 |
|
9780198506263 |
|
9780191545030 |
|
0191545031 |
|
9780191707858 |
|
0191707856 |
|
