BIRS Workshop Lecture Videos

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BIRS Workshop Lecture Videos

Simple walk in three quarter plane Trotignon, Amelie


In this talk, we consider the simple walk ($\textit{i.e.}$ walk with a set of steps {$\mathcal{S}=\{\text{W, N, E, S}\}$}) in the lattice plane. We constrain the walk to avoid the negative quadrant. The objective is to compute the number of paths $c(i,j;n)$ of length $n$, starting at $(0,0)$ and ending at $(i,j)$, with $\left(i\geq 0 \text{ or } j\geq 0\right)$ and $n\geq 0$. A way to achieve this goal is to cut the three quarters of the plane into two convex symmetric parts which will be three octants of the plane.

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