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.
Functional CLT for the range of stable random walks
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
In this note, we establish a functional central limit theorem for the capacity of the range for a class of $\alpha$-stable random walks on the integer lattice $\mathbb{Z}^d$ with $d > 5\alpha/2$. Using similar methods, we also prove an analogous result for the cardinality of the range when $d > 3\alpha / 2$.
fields
math.PR 1years
2025 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
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.