## Electronic Journal of Probability

### An Almost Sure Invariance Principle for Renormalized Intersection Local Times

#### Abstract

Let $\beta_k(n)$ be the number of self-intersections of order $k$, appropriately renormalized, for a mean zero planar random walk with $2+\delta$ moments. On a suitable probability space we can construct the random walk and a planar Brownian motion $W_t$ such that for each $k \geq 2$, $|\beta_k(n)- \gamma_k(n)|=o(1)$, a.s., where $\gamma_k(n)$ is the renormalized self-intersection local time of order $k$ at time 1 for the Brownian motion $W_{nt}/\sqrt n$.

#### Article information

Source
Electron. J. Probab., Volume 10 (2005), paper no. 4, 124-164.

Dates
Accepted: 28 February 2005
First available in Project Euclid: 1 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464816805

Digital Object Identifier
doi:10.1214/EJP.v10-236

Mathematical Reviews number (MathSciNet)
MR2120241

Zentralblatt MATH identifier
1084.60021

Rights

#### Citation

Bass, Richard; Rosen, Jay. An Almost Sure Invariance Principle for Renormalized Intersection Local Times. Electron. J. Probab. 10 (2005), paper no. 4, 124--164. doi:10.1214/EJP.v10-236. https://projecteuclid.org/euclid.ejp/1464816805

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