Tilting at windmills Tilting at windmills Tilting at windmills is an English idiom that means attacking imaginary enemies. The expression is derived from the 1605 novel "Don Quixote" by Miguel de Cervantes, and the word "tilt" in this context comes from jousting. The phrase is sometimes used to describe either confrontations where adversaries are incorrectly perceived, or courses of action that are based on misinterpreted or misapplied heroic, romantic, or idealistic justifications. It may also connote an importune, unfounded, and vain effort against adversaries real or imagined for a vain goal. The phrase comes from an episode in the Cervantes novel wherein protagonist
Tilted large deviation principle a continuous function that is bounded from above. For each Borel set "S" ⊆ "X", let and define a new family of probability measures ("ν") on "X" by Then ("ν") satisfies the large deviation principle on "X" with rate function "I" : "X" → [0, +∞] given by Tilted large deviation principle In mathematics — specifically, in large deviations theory — the tilted large deviation principle is a result that allows one to generate a new large deviation principle from an old one by "tilting", i.e. integration against an exponential functional. It can be seen as an alternative formulation of