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Despite recent observational efforts, unequivocal signs for the presence ofintermediate-mass black holes (IMBHs) in globular clusters (GCs) have not beenfound yet. Especially when the presence of IMBHs is constrained throughdynamical modeling of stellar kinematics, it is fundamental to account for thedisplacement that the IMBH might have with respect to the GC centre. In thispaper we analyse the IMBH wandering around the stellar density centre using aset of realistic direct N-body simulations of star cluster evolution. Guided bythe simulation results, we develop a basic yet accurate model that can be usedto estimate the average IMBH radial displacement ($\left<r_\mathrm{bh}\right>$)in terms of structural quantities as the core radius ($r_\mathrm{c}$), mass($M_\mathrm{c}$), and velocity dispersion ($\sigma_\mathrm{c}$), in addition tothe average stellar mass ($m_\mathrm{c}$) and the IMBH mass ($M_\mathrm{bh}$).The model can be expressed by the equation$\left<r_\mathrm{bh}\right>/r_\mathrm{c}=A(m_\mathrm{c}/M_\mathrm{bh})^\alpha[\sigma_\mathrm{c}^2r_\mathrm{c}/(GM_\mathrm{c})]^\beta$,in which the free parameters $A,\alpha,\beta$ are calculated through comparisonwith the numerical results on the IMBH displacement. The model is then appliedto Galactic GCs, finding that for an IMBH mass equal to 0.1% of the GC mass,the typical expected displacement of a putative IMBH is around $1''$ for mostGalactic GCs, but IMBHs can wander to larger angular distances in some objects,including a prediction of a $2.5''$ displacement for NGC 5139 ($\omega$ Cen),and $>10''$ for NGC 5053, NGC 6366 and ARP2.

Wandering off the centre: a characterization of the random motion of intermediate-mass black holes in star clusters