We study first passage percolation (FPP) on a Gromov-hyperbolic group G
with boundary ∂G equipped with the Patterson-Sullivan measure ν.
We associate an i.i.d.\ collection of random passage times to each edge of a
Cayley gra...
A New Analysis of Differential Privacy's Generalization Guarantees
September 8, 2019
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Computer Science
Statistics
Machine Learning
Cryptography and Security
Machine Learning
We give a new proof of the "transfer theorem" underlying adaptive data
analysis: that any mechanism for answering adaptively chosen statistical
queries that is differentially private and sample-accurate is also accurate
out-of-sample. Our n...
Rigidity results for Lp-operator algebras and applications
September 8, 2019
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Mathematics
Operator Algebras
For p∈[1,∞), we show that every unital Lp-operator algebra
contains a unique maximal C∗-subalgebra, which is always abelian if p=2. Using this, we canonically associate to every unital Lp-operator algebra
A an \'e...
Gaussian scrolls, Gaussian flags and duality
September 7, 2019
Mathematics
Algebraic Geometry
A projective variety whose Gauss map has positive dimensional fibres
corresponds to a special kind of scroll called \emph{Gaussian}. A Gaussian
scroll is a member of a canonical derived \emph{ Gaussian flag}. We introduce a
duality in the c...
The R-transform as a power map and its generalisations to higher degree
September 5, 2019
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Mathematics
Number Theory
Rings and Algebras
We give iterative constructions for irreducible polynomials over F_q of
degree nt^r for all nonnegative integers r, starting from irreducible
polynomials of degree n. The iterative constructions correspond modulo
fractional linear transform...
Elastic_HH: Tailored Elastic for Finding Heavy Hitters
September 5, 2019
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Computer Science
Networking and Internet Architecture
Finding heavy hitters has been of vital importance in network measurement.
Among all the recent works in finding heavy hitters, the Elastic sketch
achieves the highest accuracy and fastest speed. However, we find that there is
still room fo...
Gerstenhaber brackets on Hochschild cohomology of general twisted tensor
products
September 4, 2019
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Mathematics
Rings and Algebras
Representation Theory
We present techniques for computing Gerstenhaber brackets on Hochschild
cohomology of general twisted tensor product algebras. These techniques involve
twisted tensor product resolutions and are based on recent results on
Gerstenhaber brack...
Scoring Strategic Agents
September 4, 2019
Economics
Theoretical Economics
I introduce a model of predictive scoring. A receiver wants to predict a
sender's quality. An intermediary observes multiple features of the sender and
aggregates them into a score. Based on the score, the receiver makes a
decision. The sen...
The convex dimension of hypergraphs and the hypersimplicial Van
Kampen-Flores Theorem
September 3, 2019
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Mathematics
Computer Science
Combinatorics
Discrete Mathematics
The convex dimension of a k-uniform hypergraph is the smallest dimension
d for which there is an injective mapping of its vertices into Rd
such that the set of k-barycenters of all hyperedges is in convex position.
We comp...
On the cells and associated varieties of highest weight Harish-Chandra
modules
September 2, 2019
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Mathematics
Representation Theory
Let G be a Hermitian type Lie group with complexified Lie algebra
g and maximal compact subgroup K. We use L(λ) to denote
a highest weight Harish-Chandra G-module with infinitesimal character
λ. Let w be...