Cluster path limits and stationary width tails for Brownian particles with pair resetting

Brownian particles reset in pairs to a common random convex combination at rates asymptotically proportional to the inverse square of their separation. I construct their diffusive cluster limit for fixed population size in dimension d when κ > 4d, including starts that approach a collision. For three particles the first reset leaves at most two occupied sites. The gap between those sites determines a harmonic function of degree s. The centered configuration has a unique stationary law with squared-width tail π(V > t) = t^{−(s−2)/2 + o(1)}. I obtain this exponent in two ways: by comparing annular exits in the microscopic and limiting processes, and by estimating the microscopic generator directly using regularity across collisions. Both proofs allow arbitrary rates of profile convergence to one. Under an additional integrability condition on the profile errors, a direct generator estimate for the same function gives upper and lower bounds of order t^{−(s−2)/2}.