The Hitchin component is a (special) connected component of the space of homomorphisms of a surface group into $\textrm{PSL}(d,\mathbb{R}).$  This component is a higher rank analogue of the Teichmuller space of the surface.  The purpose of the talk is to show that the critical exponent of a Hitchin representation has a rigid upper bound. This is a joint work with Rafael Potrie.