Small Ball Probability, Inverse Theorems, and Applications
By Hoi H. Nguyen, Van H. Vu. 2012
104 citations recorded by the source corpus.
Let ξ be a real random variable with mean zero and variance one and A ={a 1; …; a n } be a multi-set in R d . The random sum $$S_A : = a_1 \xi _1 + \cdots + a_n \xi _n$$ where ξ i are iid copies of ξ is of fundamental importance in probability and its applications.
Subfields: Algebra and Number Theory, Applied Mathematics, Discrete Mathematics and Combinatorics
View Paper: https://www.semanticscholar.org/paper/e3ef2408ba39c2d8fa4fd9793dfd0fd1a23778f8
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In Algebra and Number Theory
- Jaouad Mourtada
- Van H. Vu
- Terence Tao
- Hoi H. Nguyen
- Nikos Frantzikinakis
- B. Host
- Ben Joseph Green
- T. Ziegler
In Applied Mathematics
- Hoi H. Nguyen
- Jaouad Mourtada
- Van H. Vu
- Terence Tao
- Raghu Meka
- Sanghyuk Lee
- Roman Vershynin
- L. Erdős
In Discrete Mathematics and Combinatorics
- Hoi H. Nguyen
- Van H. Vu
- Terence Tao
- Jaouad Mourtada
- L. Erdős
- Nicholas A. Cook
- Charles Bordenave
- Jun Yin
Citations in the corpus
- Random matrices: tail bounds for gaps between eigenvalues (2015, background): “[27], [18]) and by Rudelson and Vershynin (see e.”
- Exact minimax risk for linear least squares, and the lower tail of sample covariance matrices (2019, background): “iance. Let us introduce the Lévy concentration function QZ: R+ → [0,1] of a real random variable Zdefined by, for t>0, QZ(t) := sup a∈R P(|Z−a| 6t). Anti-concentration (or small ball probabilities) [NV13] refers to nonvacuous upper bounds on this function. Here, in order to establish Assumption 1,”
- Anti-concentration for Polynomials of Independent Random Variables (2015, background): “Thus, the Gotsman-Linial Conjecture implies the Conjecture in [19] that P(P(ξ1, .”