The paper proves functional CLTs for the range of random walks in the domain of attraction of stable laws for d/beta <= 3/2, with limits ranging from Brownian motion to renormalized self-intersection local time.
Exponential asymptotics for intersection local times of stable processes and random walks
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Functional Limit Theorems for the range of stable random walks
The paper proves functional CLTs for the range of random walks in the domain of attraction of stable laws for d/beta <= 3/2, with limits ranging from Brownian motion to renormalized self-intersection local time.