Skip to main content Accessibility help
×
Hostname: page-component-8448b6f56d-c4f8m Total loading time: 0 Render date: 2024-04-24T13:28:02.429Z Has data issue: false hasContentIssue false

18 - A final word

Published online by Cambridge University Press:  11 August 2009

Gilles Chabrier
Affiliation:
Ecole Normale Superieure, Lyon
Get access

Summary

We have heard a lot about probability functions p(M) at this meeting for mass M of planets or stars or clouds or clusters under various conditions. Since we have covered such an enormous range of masses, it is not surprising that power-law distributions close to the scale-invariant power have recurred so often. A power law differing from this distribution in the direction of favouring either low or high masses must of course have a turnover (or termination) towards this end to avoid a divergence. The physical reason for such a turnover is of interest, as is the question of continuity between the various types of objects. Bingelli and Hascher (PASP 119, 592, 2007) have followed this power-law continuity over 36 orders of magnitude in mass from asteroids to galaxy superclusters. It is instructive to look at similar probability distribution functions in quite different fields. I will give only the examples of two different kinds of human aggregates. One example, which has been discussed for more than a century or so, is the probability distribution for the size (i.e. the number of inhabitants) of a village, town or city. Near the end of the nineteenth century, the deviation from scale invariance was a slight increase towards the bottom end, i.e. overall slightly more people lived in a village of population 100-200 than in a city of 250 000 to 500 000.

Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@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.

  • A final word
  • Edited by Gilles Chabrier, Ecole Normale Superieure, Lyon
  • Book: Structure Formation in Astrophysics
  • Online publication: 11 August 2009
  • Chapter DOI: https://doi.org/10.1017/CBO9780511575198.019
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.

  • A final word
  • Edited by Gilles Chabrier, Ecole Normale Superieure, Lyon
  • Book: Structure Formation in Astrophysics
  • Online publication: 11 August 2009
  • Chapter DOI: https://doi.org/10.1017/CBO9780511575198.019
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.

  • A final word
  • Edited by Gilles Chabrier, Ecole Normale Superieure, Lyon
  • Book: Structure Formation in Astrophysics
  • Online publication: 11 August 2009
  • Chapter DOI: https://doi.org/10.1017/CBO9780511575198.019
Available formats
×