  Pairing correlations in nuclei play a decisive role in determining nuclear
drip-lines, binding energies, and many collective properties. In this work a
new Configuration-Space Monte-Carlo (CSMC) method for treating nuclear pairing
correlations is developed, implemented, and demonstrated. In CSMC the
Hamiltonian matrix is stochastically generated in Krylov subspace, resulting in
the Monte-Carlo version of Lanczos-like diagonalization. The advantages of this
approach over other techniques are discussed; the absence of the fermionic sign
problem, probabilistic interpretation of quantum-mechanical amplitudes, and
ability to handle truly large-scale problems with defined precision and error
control, are noteworthy merits of CSMC. The features of our CSMC approach are
shown using models and realistic examples. Special attention is given to
difficult limits: situations with non-constant pairing strengths, cases with
nearly degenerate excited states, limits when pairing correlations in finite
systems are weak, and problems when the relevant configuration space is large.
