We define new -invariants which we call secondary Novikov-Shubin invariants.We calculate the first secondary Novikov-Shubin invariants of finitely generated groups by using random walk on Cayley graphs and see in particular that these are invariant under quasi-isometry.
Shin-ichi OGUNI. "Secondary Novikov-Shubin invariants of groups and quasi-isometry." J. Math. Soc. Japan 59 (1) 223 - 237, January, 2007. https://doi.org/10.2969/jmsj/1180135508