  We explain the microscopic origin of linear confinement potential with the
Casimir scaling in generic confining gauge theories. In the low-temperature
regime of confining gauge theories such as QCD, Polyakov lines are slowly
varying Haar random modulo exponentially small corrections with respect to the
inverse temperature, as shown by one of the authors (M.~H.) and Watanabe. With
exact Haar randomness, computation of the two-point correlator of Polyakov
loops reduces to the problem of random walk on group manifold. Linear
confinement potential with approximate Casimir scaling except at short
distances follows naturally from slowly varying Haar randomness. With
exponentially small corrections to Haar randomness, string breaking and loss of
Casimir scaling at long distance follow. Hence we obtain the Casimir scaling
which is only approximate and holds only at intermediate distance, which is
precisely needed to explain the results of lattice simulations. For
$(1+1)$-dimensional theories, there is a simplification that admits the Casimir
scaling at short distances as well.
