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- Gregory F. Lawler, Emily E. Puckette
- Combinatorics, Probability & Computing
- 2000

The intersection exponent for simple random walk in two and three dimensions gives a measure of the rate of decay of the probability that paths do not intersect. In this paper we show that the intersection exponent for random walks is the same as that for Brownian motion and show in fact that the probability of nonintersection up to distance n is comparable… (More)

Using Monte-Carlo simulations, we estimate numerically disconnection exponents for planar Brownian motions. These simulations tend to confirm conjectures by Duplantier and Mandelbrot.

Using Monte-Carlo simulations, we estimate numerically disconnec-tion exponents for planar Brownian motions. These simulations tend to connrm conjectures by Duplantier and Mandelbrot.

Using Monte-Carlo simulations, we estimate numerically disconnection exponents for planar Brownian motions. These simulations tend to connrm conjectures by Duplantier and Mandel-brot.

We create a simple discrete probabilistic model for spread of a forest fire. We examine the conditions for which the fire will either die out or spread indefinitely, identifying and bounding a critical value for the probability of transmission of the fire to an immediately adjacent location. PREREQUISITES: Summation of geometric series, elementary… (More)

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