  Monte Carlo dynamics of the lattice 48 monomers toy protein is interpreted as
a random walk in an abstract (discrete) space of conformations. To test the
geometry of this space, we examine the return probability $P(T)$, which is the
probability to find the polymer in the native state after $T$ Monte Carlo
steps, provided that it starts from the native state at the initial moment.
Comparing computational data with the theoretical expressions for $P(T)$ for
random walks in a variety of different spaces, we show that conformational
spaces of polymer loops may have non-trivial dimensions and exhibit negative
curvature characteristic of Lobachevskii (hyperbolic) geometry.
