  Supermassive black holes in the centre of galaxies dominate the gravitational
potential of their surrounding stellar clusters. In these dense environments,
stars follow nearly Keplerian orbits, which get slowly distorted as a result of
the potential fluctuations generated by the stellar cluster itself as a whole.
In particular, stars undergo a rapid relaxation of their eccentricities through
both resonant and non-resonant processes. An efficient implementation of the
resonant diffusion coefficients allows for detailed and systematic explorations
of the parameter space describing the properties of the stellar cluster. In
conjunction with recent observations of the S-cluster orbiting SgrA*, this
framework can be used to jointly constrain the distribution of the unresolved,
old, background stellar cluster and the characteristics of a putative dark
cluster. Specifically, we show how this can be used to estimate the typical
mass and cuspide exponent of intermediate-mass black holes consistent with the
relaxed state of the distribution of eccentricities in the observed S-cluster.
This should prove useful in constraining super massive black hole formation
scenarios.
