  We consider two random walkers starting at the same time $t=0$ from different
points in space separated by a given distance $R$. We compute the average
volume of the space visited by both walkers up to time $t$ as a function of $R$
and $t$ and dimensionality of space $d$. For $d<4$, this volume, after proper
renormalization, is shown to be expressed through a scaling function of a
single variable $R/\sqrt{t}$. We provide general integral formulas for scaling
functions for arbitrary dimensionality $d<4$. In contrast, we show that no
scaling function exists for higher dimensionalities $d \geq 4$
