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The incipient infinite cluster in high-dimensional percolation
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## Asymptotic results for super-Brownian motions and
semilinear differential equations

### Tzong-Yow Lee

**Abstract.**
Limit laws for three-dimensional super-Brownian motion are
derived, conditioned on survival up to a large time.
A large deviation principle is proved for the
joint behavior of occupation times and their difference.
These are done via analyzing the generating function and
exploiting a connection between probability and differential/integral
equations.

*Copyright 1998 American Mathematical Society*

**Retrieve entire article **

#### Article Info

- ERA Amer. Math. Soc.
**04** (1998), pp. 56-62
- Publisher Identifier: S 1079-6762(98)00048-1
- 1991
*Mathematics Subject Classification*. Primary 60B12, 60F10
*Key words and phrases*. Large deviations, occupation time,
measure-valued process, branching Brownian motion, semilinear PDE,
asymptotics
- Received by the editors March 17
- Posted on September 14, 1998
- Communicated by Mark Freidlin
- Comments (When Available)

**Tzong-Yow Lee**

University of Maryland, College Park, MD

*E-mail address:* `tyl@math.umd.edu`

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