Skip to main content Accessibility help
×
  1. Home
  2. Browse subjects
  3. Computer Science
  4. Algorithmics, Complexity, Computer Algebra, Computational Geometry
  5. Content listing

Refine search

Refine search

Access:
Content type:
Publication date:
Apply   From and To filters
Subject: Show more
Journals Show more
Publishers: Show more
Societies Show more
Series: Show more
Collections: Show more

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

6974 results in Algorithmics, Complexity, Computer Algebra, Computational Geometry

Page 121 of 349

  • Convergence of Achlioptas Processes via Differential Equations with Unique Solutions

  • Part of
  • OLIVER RIORDAN, LUTZ WARNKE
  • Journal:
    Combinatorics, Probability and Computing / Volume 25 / Issue 1 / January 2016
    Published online by Cambridge University Press:
    14 October 2015, pp. 154-171

  • In Achlioptas processes, starting from an empty graph, in each step two potential edges are chosen uniformly at random, and using some rule one of them is selected and added to the evolving graph. The evolution of the rescaled size of the largest component in such variations of the Erdős–Rényi random graph process has recently received considerable attention, in particular for Bollobás's ‘product rule’. In this paper we establish the following result for rules such as the product rule: the limit of the rescaled size of the ‘giant’ component exists and is continuous provided that a certain system of differential equations has a unique solution. In fact, our result applies to a very large class of Achlioptas-like processes.

    Our proof relies on a general idea which relates the evolution of stochastic processes to an associated system of differential equations. Provided that the latter has a unique solution, our approach shows that certain discrete quantities converge (after appropriate rescaling) to this solution.

Page 121 of 349