A Geometric Interpretation of Half-Plane Capacity (2009)
Lalley, Steven, Lawler, Gregory, Narayanan, Hariharan
Let A be a bounded, relatively closed subset of the upper half plane H whose complement C is simply connected. If B_t is a standard complex Brownian motion starting at iy and t_A = inf {t > 0: B_t...
Conformal invariance, universality, and the dimension of the Brownian frontier (2003)
This paper describes joint work with Oded Schramm and Wendelin Werner establishing the values of the planar Brownian intersection exponents from which one derives the Hausdorff dimension of certain...
Conformal restriction: the chordal case (2002)
Lawler, Gregory, Schramm, Oded, Werner, Wendelin
We characterize and describe all random subsets $K$ of a given simply connected planar domain (the upper half-plane $\H$, say) which satisfy the ``conformal restriction'' property, i.e., $K$ connects...
The Intersection Exponent for Simple Random Walk (1998)
Gregory Lawler, Emily E. Puckette
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...
Loop-Erased Walks Intersect Infinitely Often In Four Dimensions (1998)
In this short note we show that the paths two independent loop-erased random walks in four dimensions intersect infinitely often. We actually prove the stronger result that the cut-points of the two...
Loop-Erased Walks Intersect Infinitely Often In Four Dimensions (1998)
In this short note we show that the paths two independent loop-erased random walks in four dimensions intersect infinitely often. We actually prove the stronger result that the cut-points of the two...
The Frontier of a Brownian Path Is Multifractal (1997)
We consider the multifractal spectrum of harmonic measure of a Brownian motion path in two or three dimensions. We show that the multifractal spectrum is nontrivial and relate the spectrum to the...
Multifractal Nature of Two Dimensional Simple Random Walk Paths (1997)
The multifractal spectrum of discrete harmonic measure of a two dimensional simple random walk path is considered. It is shown that the spectrum is the same as for Brownian motion, is nontrivial, and...
Cut Times for Simple Random Walk (1996)
: Let S(n) be a simple random walk taking values in Z d . A time n is called a cut time if S[0; n] " S[n + 1; 1) = ;: We show that in three dimensions the number of cut times less than n grows...