Abstract
We study sequences of random variables obtained by iterative procedures, which can be thought of as nonlinear generalizations of the arithmetic mean. We prove a strong law of large numbers for a class of such iterations. This gives rise to the concept of generalized expected value of a random variable, for which we prove an analog of the classical Jensen inequality. We give several applications to models arising in mathematical physics and other areas.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1373-1384 |
| Number of pages | 12 |
| Journal | Journal of Statistical Physics |
| Volume | 86 |
| Issue number | 5-6 |
| DOIs | |
| State | Published - Mar 1997 |
Keywords
- Disordered systems
- Hierarchical models
- Law of large numbers
- Martingales
- Self-averaging
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
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