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 Contact Process on a Finite Set. III: The Critical Case

Richard Durrett, Roberto H. Schonmann and Nelson I. Tanaka
The Annals of Probability
Vol. 17, No. 4 (Oct., 1989), pp. 1303-1321
Stable URL: http://www.jstor.org/stable/2244437
Page Count: 19
  • 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 Contact Process on a Finite Set. III: The Critical Case
Preview not available

Abstract

We show that if σN is the time that the contact process on {1, ... N} first hits the empty set then for λ = λc, the critical value for the contact process on Z, σN/N → ∞ and σN/N4 → 0 in probability as N → ∞. The keys to the proof are a new renormalized bond construction and lower bounds for the fluctuations of the right edge. As a consequence of the result we get bounds on some critical exponents. We also study the analogous problem for bond percolation in {1,... N} × Z and investigate the limit distribution of σN/EσN.

Page Thumbnails

  • Thumbnail: Page 
1303
    1303
  • Thumbnail: Page 
1304
    1304
  • Thumbnail: Page 
1305
    1305
  • Thumbnail: Page 
1306
    1306
  • Thumbnail: Page 
1307
    1307
  • Thumbnail: Page 
1308
    1308
  • Thumbnail: Page 
1309
    1309
  • Thumbnail: Page 
1310
    1310
  • Thumbnail: Page 
1311
    1311
  • Thumbnail: Page 
1312
    1312
  • Thumbnail: Page 
1313
    1313
  • Thumbnail: Page 
1314
    1314
  • Thumbnail: Page 
1315
    1315
  • Thumbnail: Page 
1316
    1316
  • Thumbnail: Page 
1317
    1317
  • Thumbnail: Page 
1318
    1318
  • Thumbnail: Page 
1319
    1319
  • Thumbnail: Page 
1320
    1320
  • Thumbnail: Page 
1321
    1321