Escape times in interacting biased random walks

The dynamics of N particles with hard core exclusion performing biased random walks is studied on a one-dimensional lattice with a reflecting wall. The bias is toward the wall and the particles are placed initially on the N sites of the lattice closest to the wall. For N=1 the leading behavior of the first passage time T<SUB>FP</SUB> to a distant site l is known to follow the Kramers escape time formula T <SUB>FP</SUB>~&#955;<SUP>1</SUP> where &#955; is the ratio of hopping rates toward and away from the wall. For N &gt;1 Monte Carlo and analytical results are presented to show that for the particle closest to the wall, the Kramers formula generalizes to T<SUB>FR</SUB>~ &#955; <SUP>IN</SUP>. First passage times for the other particles are studied as well. A second question that is studied pertains to survival times T <SUB>s </SUB>in the presence of an absorbing barrier placed at site l. In contrast to the first passage time, it is found that T<SUB> s</SUB> follows the leading behavior &#955;<SUP> 1</SUP>independent of N