  We use the generic chaining device proposed by Talagrand to establish
exponential bounds on the deviation probability of some suprema of random
processes. Then, given a random vector $\xi$ in $\R^{n}$ the components of
which are independent and admit a suitable exponential moment, we deduce a
deviation inequality for the squared Euclidean norm of the projection of $\xi$
onto a linear subspace of $\R^{n}$. Finally, we provide an application of such
an inequality to statistics, performing model selection in the regression
setting when the errors are possibly non-Gaussian and the collection of models
possibly large.
