definitions of $\mathcal{F}$, and in the LDC model (which is discussed in the next section) it satisfies the following relation $$F(x,Q^2)=\int^{Q^2} \frac{dk_{\perp}^2}{k_{\perp}^2} \mathcal{F}(x,k_{\perp}^2) + 
\int_{Q^2} \frac{dk_{\perp}^2}{k_{\perp}^2} \mathcal{F}(x\frac{k_\perp^2}{Q^2},k_{\perp}^2)\frac{Q^2}{k_\perp^2}$$

The kernel of the integral, $K$, in equation , is known as the BFKL kernel. The important thing here is to find the eigenvalues of this kernel. To leading order in $\textrm{ln}(1/x)$, and for a fixed coupling constant $\alpha _S$, the largest eigenvalue is given by $\lambda = 12\alpha _S \log (2)/\pi$. It can then be shown that the gluon distribution function is given by $$G \sim \sum _{n} \frac{(\lambda \log (1/x))^n}{n!} = x^{- \lambda}$$

We will come back to the BFKL equation, and the so called BFKL pomeron, later when we discuss saturation. For now, one can note that BFKL and DGLAP are applicable in different regions. In the next section we will describe two models which interpolate between these two different regions, thus containing both the DGLAP and the BFKL physics.

### CCFM and the LDC Models

The first such model was proposed by Catani, Ciafaloni, Fiorani and Marchesini and is thus called the CCFM model. We will discuss purely gluonic chains and the last gluon in the chain is assumed 