Large Deviations of Empirical Measures of Zeros of Random Polynomials

2010 ◽  
Author(s):  
O. Zeitouni ◽  
S. Zelditch
Keyword(s):  
Large Deviations ◽  
Random Polynomials ◽  
Empirical Measures

On large deviations of empirical measures in the τ-topology

1994 ◽  
Vol 31 (A) ◽  
pp. 41-47 ◽  
Author(s):  
A. De Acosta
Keyword(s):  
Large Deviations ◽  
State Space ◽  
The State ◽  
Probability Measures ◽  
Empirical Measures

We prove a generalization of Sanov's theorem in which the state space S is arbitrary and the set of probability measures on S is endowed with the τ -topology.

A large deviations heuristic made precise

2000 ◽  
Vol 128 (3) ◽  
pp. 561-569 ◽  
Author(s):  
NEIL O'CONNELL
Keyword(s):  
Large Deviations ◽  
Bin Packing ◽  
Symmetric Functions ◽  
Large Deviation ◽  
Random Variables ◽  
Packing Problem ◽  
Rate Function ◽  
Empirical Measures ◽  
Underlying Distribution ◽  
Uniformly Lipschitz

Sanov's Theorem states that the sequence of empirical measures associated with a sequence of i.d.d. random variables satisfies the large deviation principle (LDP) in the weak topology with rate function given by a relative entropy. We present a derivative which allows one to establish LDPs for symmetric functions of many i.d.d. random variables under the condition that (i) a law of large numbers holds whatever the underlying distribution and (ii) the functions are uniformly Lipschitz. The heuristic (of the title) is that the LDP follows from (i) provided the functions are ‘sufficiently smooth’. As an application, we obtain large deviations results for the stochastic bin-packing problem.

On large deviations of empirical measures in the τ-topology

1994 ◽  
Vol 31 (A) ◽  
pp. 41-47 ◽  
Author(s):  
A. De Acosta
Keyword(s):  
Large Deviations ◽  
State Space ◽  
The State ◽  
Probability Measures ◽  
Empirical Measures

We prove a generalization of Sanov's theorem in which the state space S is arbitrary and the set of probability measures on S is endowed with the τ -topology.

scholarly journals Large deviations for bootstrapped empirical measures

Bernoulli ◽  
2014 ◽  
Vol 20 (4) ◽  
pp. 1845-1878 ◽  
Author(s):  
José Trashorras ◽  
Olivier Wintenberger
Keyword(s):  
Large Deviations ◽  
Empirical Measures
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