Skip to main content Accessibility help
×
Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-13T09:14:44.131Z Has data issue: false hasContentIssue false

1 - Introduction

Published online by Cambridge University Press:  14 December 2023

Sébastien Roch
Affiliation:
University of Wisconsin, Madison
HTML view is not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

Summary

In this chapter, we describe a few discrete probability models to which we will come back repeatedly throughout the book. While there exists a vast array of well-studied random combinatorial structures (permutations, partitions, urn models, Boolean functions, polytopes, etc.), our focus is primarily on a limited number of graph-based processes, namely percolation, random graphs, Ising models, and random walks on networks. We will not attempt to derive the theory of these models exhaustively here. Instead we will employ them to illustrate some essential techniques from discrete probability. Note that the toolkit developed in this book is meant to apply to other probabilistic models of interest as well, and in fact many more will be encountered along the way. After a brief review of graph basics and Markov chains theory, we formally introduce our main models. We also formulate various key questions about these models that will be answered (at least partially) later on. We assume that the reader is familiar with the measure-theoretic foundations of probability. A refresher of all required concepts and results is provided in the appendix.

Type
Chapter
Information
Modern Discrete Probability
An Essential Toolkit
, pp. 1 - 20
Publisher: Cambridge University Press
Print publication year: 2024

Save book to Kindle

To save this book to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

  • Introduction
  • Sébastien Roch, University of Wisconsin, Madison
  • Book: Modern Discrete Probability
  • Online publication: 14 December 2023
  • Chapter DOI: https://doi.org/10.1017/9781009305129.002
Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

  • Introduction
  • Sébastien Roch, University of Wisconsin, Madison
  • Book: Modern Discrete Probability
  • Online publication: 14 December 2023
  • Chapter DOI: https://doi.org/10.1017/9781009305129.002
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Introduction
  • Sébastien Roch, University of Wisconsin, Madison
  • Book: Modern Discrete Probability
  • Online publication: 14 December 2023
  • Chapter DOI: https://doi.org/10.1017/9781009305129.002
Available formats
×