101 Chapter 4: Fluctuations in Jet Tomography initial Q distributions as in Eq. (4.4). In this case The branching implementation is seen via the product of two distinct factors in contrast to the one quenching factor in Eq. (4.4). For small 〈 ϵ r,e Q 〉 both approaches obviously give rise to the same R$_{Q}$ = 1 − n 〈 ϵ$_{Q}$ 〉 . In both approaches, fluctuations of the radiative energy loss due to gluon number fluctuations are computed as discussed in detail in Ref. [374, 387]. This involves using the DGLV generalization [278] of the GLV opacity ex- pansion [274] to heavy quarks. Bjorken longitudinal expansion is taken into account by evaluating the bulk density at an average time τ = L/ 2 [374, 387]. For elastic energy loss fluctuations, the full Fokker-Planck solution applica- ble for small fractional energy loss is approximated by a Gaussian centered at the average loss with variance σ 2 el = 2 T 〈 Δ E $^{el}$( p$_{T}$ , L ) 〉 [249]. In approach I the correct, numerically intensive integration through the Bjorken expanding medium provides Δ E $^{el}$( p$_{T}$ , L ). In approach II the τ = L/ 2 approximation is again used; numerical comparisons show that for L ∼ 2 − 7 fm this reproduces the full calculation well. Finally, we note that we use the additional numerical simplification of keeping the strong coupling constant α$_{S}$ fixed at 0 . 3. R II $_{Q}$( p$_{⊥}$, L$_{Q}$ ) ≡ 〈 (1 − ϵ r $_{Q}$( L$_{Q}$ )) $^{n}$(1 − ϵ e $_{Q}$( L$_{Q}$ )) $^{n}$〉$_{Δ}$$_{E}$ . (4.7)