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Consider the partition function of a directed polymer in an IID

field. Under some mild assumptions on the field, it is a well-known fact

that the free energy of the polymer is equal to some deterministic constant

for almost every realization of the

field and that the upper tail large deviations is exponential. In this

talk I'll discuss the lower tail large deviations and present a method

for estimating it. As a consequence, I'll show that the lower

tail large deviations exhibits three regimes, determined by the

tail of the negative part of the field. The method applies to other

oriented models and can be adapted to non-oriented models as well. This

work extends the results of a recent paper by Cranston Gautier and

Mountford. A preprint is availabe on www.math.uci.edu/~ibenari