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.

Products of 2 × 2 Random Matrices

David Mannion
The Annals of Applied Probability
Vol. 3, No. 4 (Nov., 1993), pp. 1189-1218
Stable URL: http://www.jstor.org/stable/2245205
Page Count: 30
  • 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.
Products of 2 × 2 Random Matrices
Preview not available

Abstract

The notion of the shape of a triangle can be used to define the shape of a 2 × 2 real matrix; we find that the shape of a matrix retains just the right amount of information required for determining the main features of the asymptotic behaviour, as n→∞, of GnGn-1⋯G1, where the Gi are i.i.d. copies of a 2 × 2 random matrix G. An alternative formula to the Furstenberg formula is proposed for the upper Lyapounov exponent of the probability distribution of G. We find that in some cases, using our formula, the Lyapounov exponent is more susceptible to explicit calculation.

Page Thumbnails

  • Thumbnail: Page 
1189
    1189
  • Thumbnail: Page 
1190
    1190
  • Thumbnail: Page 
1191
    1191
  • Thumbnail: Page 
1192
    1192
  • Thumbnail: Page 
1193
    1193
  • Thumbnail: Page 
1194
    1194
  • Thumbnail: Page 
1195
    1195
  • Thumbnail: Page 
1196
    1196
  • Thumbnail: Page 
1197
    1197
  • Thumbnail: Page 
1198
    1198
  • Thumbnail: Page 
1199
    1199
  • Thumbnail: Page 
1200
    1200
  • Thumbnail: Page 
1201
    1201
  • Thumbnail: Page 
1202
    1202
  • Thumbnail: Page 
1203
    1203
  • Thumbnail: Page 
1204
    1204
  • Thumbnail: Page 
1205
    1205
  • Thumbnail: Page 
1206
    1206
  • Thumbnail: Page 
1207
    1207
  • Thumbnail: Page 
1208
    1208
  • Thumbnail: Page 
1209
    1209
  • Thumbnail: Page 
1210
    1210
  • Thumbnail: Page 
1211
    1211
  • Thumbnail: Page 
1212
    1212
  • Thumbnail: Page 
1213
    1213
  • Thumbnail: Page 
1214
    1214
  • Thumbnail: Page 
1215
    1215
  • Thumbnail: Page 
1216
    1216
  • Thumbnail: Page 
1217
    1217
  • Thumbnail: Page 
1218
    1218