Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.

The Second Lowest Extremal Invariant Measure of the Contact Process II

Marcia Salzano and Roberto H. Schonmann
The Annals of Probability
Vol. 27, No. 2 (Apr., 1999), pp. 845-875
Stable URL: http://www.jstor.org/stable/2652764
Page Count: 31
  • Read Online (Free)
  • Download ($19.00)
  • Subscribe ($19.50)
  • Cite this Item
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
The Second Lowest Extremal Invariant Measure of the Contact Process II
Preview not available

Abstract

We continue the investigation of the behavior of the contact process on infinite connected graphs of bounded degree. Some questions left open by Salzano and Schonmann (1997) concerning the notions of complete convergence, partial convergence and the criterion r = s are answered. The continuity properties of the survival probability and the recurrence probability are studied. These order parameters are found to have a richer behavior than expected, with the possibility of the survival probability being discontinuous at or above the threshold for survival. A condition which guarantees the continuity of the survival probability above the survival point is introduced and exploited. The recurrence probability is shown to always be left-continuous above the recurrence point, and a necessary and sufficient condition for its right-continuity is introduced and exploited. It is shown that for homogeneous graphs the survival probability can only be discontinuous at the survival point, and the recurrence probability can only be discontinuous at the recurrence point. For graphs which are obtained by joining a finite number of severed homogeneous trees by means of a finite number of vertices and edges, the survival point, the recurrence point and the discontinuity points of the survival and recurrence probabilities are located.

Page Thumbnails

  • Thumbnail: Page 
845
    845
  • Thumbnail: Page 
846
    846
  • Thumbnail: Page 
847
    847
  • Thumbnail: Page 
848
    848
  • Thumbnail: Page 
849
    849
  • Thumbnail: Page 
850
    850
  • Thumbnail: Page 
851
    851
  • Thumbnail: Page 
852
    852
  • Thumbnail: Page 
853
    853
  • Thumbnail: Page 
854
    854
  • Thumbnail: Page 
855
    855
  • Thumbnail: Page 
856
    856
  • Thumbnail: Page 
857
    857
  • Thumbnail: Page 
858
    858
  • Thumbnail: Page 
859
    859
  • Thumbnail: Page 
860
    860
  • Thumbnail: Page 
861
    861
  • Thumbnail: Page 
862
    862
  • Thumbnail: Page 
863
    863
  • Thumbnail: Page 
864
    864
  • Thumbnail: Page 
865
    865
  • Thumbnail: Page 
866
    866
  • Thumbnail: Page 
867
    867
  • Thumbnail: Page 
868
    868
  • Thumbnail: Page 
869
    869
  • Thumbnail: Page 
870
    870
  • Thumbnail: Page 
871
    871
  • Thumbnail: Page 
872
    872
  • Thumbnail: Page 
873
    873
  • Thumbnail: Page 
874
    874
  • Thumbnail: Page 
875
    875