@article{EJP1719,
author = {Denis Denisov and Vitali Wachtel},
title = {Ordered random walks with heavy tails},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {17},
year = {2012},
keywords = {Dyson's Brownian Motion; Doob \$h\$-transform; superharmonic function; Weyl chamber; Martin boundary},
abstract = {This note continues paper of Denisov and Wachtel (2010), where we have constructed a $k$-dimensional random walk conditioned to stay in the Weyl chamber of type $A$. The construction was done under the assumption that the original random walk has $k-1$ moments. In this note we continue the study of killed random walks in the Weyl chamber, and assume that the tail of increments is regularly varying of index $\alpha<k-1$. It appears that the asymptotic behaviour of random walks is different in this case. We determine the asymptotic behaviour of the exit time, and, using this information, construct a conditioned process which lives on a partial compactification of the Weyl chamber.},
pages = {no. 4, 1-21},
issn = {1083-6489},
doi = {10.1214/EJP.v17-1719},
url = {http://ejp.ejpecp.org/article/view/1719}}