I have seen references to the "tilting method" in the theory of large deviations. Is there a simple explanation of what this is, exactly?



What is "tilting" in the context of large deviations?
Tilting refers to a change of measure of the form $e^{\lambda \cdot x}/C(\lambda)$ where $C(\lambda)=E(e^{\lambda\cdot X})$.
(The setup is that the measure for which you are proving large deviations is a topological vector space $X$, and $\lambda$ is in the dual space to $X$). The name tilting comes because the effect of the change of measure translates to modifying the ``typical behavior'' under the tilted measure; more technically, the tilting adds a linear term to the log-moment generating function, and that translates to a linear shift in the corresponding Legendre transform that will represent the rate function.


EDIT (in response to Igor's further question in comment): The reason you change measure is the following. You are trying to compute $P\_n(A)$ which is small. Write now 
$$P\_n(A)=\int\_A dQ\_n (dP\_n/dQ\_n)$$
and choose $Q\_n$ such that $Q\_n(A)$ is large (i.e., make $A$ "typical", so that $n^{-1}\log Q\_n(A)\sim 0$). Now if $(dP\_n/dQ\_n)$ is almost constant on $A$, say equal $e^{-nJ}$, then you are happy because
then $P\_n(A)\sim e^{-nJ} Q\_n(A)$. The devil is in the details of the words ``almost constant'' and $\sim$ but this is roughly the idea. 


