منابع مشابه
Corrections and Additions to “entropy of Quantum Limits” Jean Bourgain and Elon Lindenstrauss
This theorem implies that every ergodic component of a quantum limit μ under the flow a(t) has entropy ≥ κ′. In a later paper [2], the second named author has been able to use Theorem 1 in conjunction with a partial classification of measures on X invariant under the geodesic flow that satisfy a recurrence property under the Hecke correspondence to prove that the only arithmetic quantum limit i...
متن کاملToward a Unified Theory of Sparse Dimensionality Reduction in Euclidean Space Jean Bourgain and Jelani Nelson
Let Φ ∈ Rm×n be a sparse Johnson-Lindenstrauss transform [KN] with s non-zeroes per column. For T a subset of the unit sphere, ε ∈ (0, 1/2) given, we study settings for m, s required to ensure E Φ sup x∈T ∣∣‖Φx‖22 − 1∣∣ < ε, i.e. so that Φ preserves the norm of every x ∈ T simultaneously and multiplicatively up to 1 + ε. In particular, our most general theorem shows that it suffices to set m = ...
متن کاملRemembering remembering.
We developed a laboratory analogue of the "forgot-it-all-along" effect that J. W. Schooler, M. Bendiksen, and Z. Ambadar (1997) proposed for cases of "recovered memories" in which individuals had forgotten episodes of talking about the abuse when they were supposedly amnestic for it. In Experiment 1, participants studied homographs with disambiguating context words; in Test 1 they received stud...
متن کاملBourgain ’ s Theorem
Exercise 1. Show that distances between sets do not necessarily satisfy the triangle inequality. That is, it is possible that d(S1, S2) + d(S2, S3) > d(S1, S3) for some sets S1, S2 and S3. Exercise 2. Prove that d(x, y) ≥ d(S, x)− d(S, y) and thus d(x, y) ≥ |d(S, x)− d(S, y)|. Proof. Fix ε > 0. Let y′ ∈ S be such that d(y′, y) ≤ d(S, y) + ε (if S is a finite set, there is y′ ∈ S s.t. d(y, y′) =...
متن کاملOn a Question of Bombieri and Bourgain
(1) an n+1-tuple (ρ, χ1, ...., χn) of nontrivial C×-valued multiplicative characters of k×, each extended to k by the requirement that it vanish at 0 ∈ k. (2) an n+1-tuple (g, f1, ...., fn) of nonzero one-variable k-polynomials, which are adapted to the character list above in the following sense. Whenever α ∈ k is a zero of g (respectively of some fi), then ρα (respectively χ ordα(fi) i ) is n...
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ژورنال
عنوان ژورنال: Notices of the American Mathematical Society
سال: 2021
ISSN: 0002-9920,1088-9477
DOI: 10.1090/noti2290