Reunion probabilities of $N$ one-dimensional random walkers with mixed boundary conditions

Understand

In this work we extend the results of the reunion probability of $N$ one-dimensional random walkers to include mixed boundary conditions between their trajectories.

• The level of the mixture is controlled by a parameter $c$, which can be varied from $c=0$ (independent walkers) to $c\to\infty$ (vicious walkers).
• The expressions are derived by using Quantum Mechanics formalism (QMf) which allows us to map this problem into a Lieb-Liniger gas (LLg) of $N$ one-dimensional particles.
• We use Bethe ansatz and Gaudin's conjecture to obtain the normalized wave-functions and use this information to construct the propagator.