Displaying similar documents to “Conditional principles for random weighted measures”

Entropic Projections and Dominating Points

Christian Léonard (2010)

ESAIM: Probability and Statistics

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Entropic projections and dominating points are solutions to convex minimization problems related to conditional laws of large numbers. They appear in many areas of applied mathematics such as statistical physics, information theory, mathematical statistics, ill-posed inverse problems or large deviation theory. By means of convex conjugate duality and functional analysis, criteria are derived for the existence of entropic projections, generalized entropic projections and dominating...

Large deviations for independent random variables – Application to Erdös-Renyi’s functional law of large numbers

Jamal Najim (2005)

ESAIM: Probability and Statistics

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A Large Deviation Principle (LDP) is proved for the family 1 n 1 n 𝐟 ( x i n ) · Z i n where the deterministic probability measure 1 n 1 n δ x i n converges weakly to a probability measure R and ( Z i n ) i are d -valued independent random variables whose distribution depends on x i n and satisfies the following exponential moments condition: sup i , n 𝔼 e α * | Z i n | < + forsome 0 < α * < + . In this context, the identification of the rate function is non-trivial due to the absence of equidistribution. We rely on fine convex analysis to address this issue. Among...

Directed polymer in random environment and last passage percolation

Philippe Carmona (2010)

ESAIM: Probability and Statistics

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The sequence of random probability measures that gives a path of length , 1 n times the sum of the random weights collected along the paths, is shown to satisfy a large deviations principle with good rate function the Legendre transform of the free energy of the associated directed polymer in a random environment. Consequences on the asymptotics of the typical number of paths whose collected weight is above a fixed proportion are then drawn.