Exact results for vicious walker models of domain walls

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Abstract
Non-intersecting (or vicious) random walker models in one dimension can be interpreted as models of domain walls in two dimensions. Three problems pertaining to vicious walker models are solved. The first is the exact evaluation of the partition function for the random turns model of vicious walkers on a lattice. In this model, at each tick of the clock, a randomly chosen walker must move one step to the left or one step to the right. The second problem is the calculation of the mean spacing between walls in terms of the chemical potential for a Brownian motion model of continuous domain walls in a strip, while the final problem solved is the calculation of the correlation between defects, which occur when two domain walls meet and end without crossing the whole system.