Meaning of $\wedge$ in this equation

Question

What is $\{ \rho( \xi_n, \xi) \wedge 1\}$ in the following equation?

Answer 1

The wedge symbol $\wedge$ is sometimes used to mean this function

$$ (f\wedge g)(x) \;\; =\;\; \min\{f(x), g(x)\} $$

which is defined at each point $x$. This can actually be expressed equivalently as:

$$ (f\wedge g)(x) \;\; =\;\; \frac{1}{2}\left [f(x) + g(x) - |f(x) - g(x)| \right ]. $$

In your particular example, it appears that the context in which they present it is the minimum between the distance of two random elements and the constant 1: $$ \rho(\xi_n, \xi) \wedge 1 \;\; =\;\; \min\{\rho(\xi_n, \xi), 1\}. $$