Multiplicative arithmetic functions and the generalized Ewens measure
September 2, 2019
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Mathematics
Number Theory
Probability
Random integers, sampled uniformly from [1,x], share similarities with
random permutations, sampled uniformly from Sn​. These similarities include
the Erd\H{o}s--Kac theorem on the distribution of the number of prime factors
of a random...
The Lubin-Tate Theory of Configuration Spaces: I
August 29, 2019
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Mathematics
Algebraic Topology
Geometric Topology
We construct a spectral sequence converging to the Morava E-theory of
unordered configuration spaces and identify its E2-page as the homology of a
Chevalley-Eilenberg-like complex for Hecke Lie algebras. Based on this, we
compute the $...
Eliminating Left Recursion without the Epsilon
August 28, 2019
Computer Science
Data Structures and Algorithms
The standard algorithm to eliminate indirect left recursion takes a
preventative approach, rewriting a grammar's rules so that indirect left
recursion is no longer possible, rather than eliminating it only as and when it
occurs. This approa...
Phase transitions and composite order in U(1)N lattice
London models
August 28, 2019
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Physics
Strongly Correlated Electrons
Superconductivity
The phase diagrams and the nature of the phase transitions in multicomponent
gauge theories with an Abelian gauge field are important topics with various
physical applications. While an early renormalization-group-based study
indicated that...
Entropy Gain and Information Loss by Measurements
August 27, 2019
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Physics
Mathematics
Quantum Physics
Mathematical Physics
Mathematical Physics
Probability
Quantum Physics
Mathematical Physics
Mathematical Physics
Probability
When the quantum entropy (QE) of a system increases due to measurements, it
leads to the loss of certain information, part of which may be recoverable. We
define Information Loss (IL) as a function of the density matrix through
quantum entr...
Treatise on Differential Geometry and its role in Relativity Theory
August 27, 2019
Physics
General Relativity and Quantum Cosmology
This lecture note is hopefully helpful to undergraduate and postgraduate
students or beginning Ph.D students both in theoretical physics and in applied
mathematics. Modern terminology in differential geometry has been discussed in
the book ...
A Note on The Gaussian Moat Problem
August 27, 2019
Mathematics
Number Theory
The Gaussian moat problem asks whether it is possible to find an infinite
sequence of distinct Gaussian prime numbers such that the difference between
consecutive numbers in the sequence is bounded. In this paper, we have proved
that the an...
A universal characterization of standard Borel spaces
August 27, 2019
Mathematics
Logic
Category Theory
We prove that the category SBor of standard Borel spaces is the
(bi-)initial object in the 2-category of countably complete Boolean (countably)
extensive categories. This means that SBor is the universal category
admit...
On the Onsager-Machlup functional for the Brownian motion on the
Heisenberg group
August 24, 2019
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Mathematics
Probability
Probability
Onsager-Machlup functionals are used to describe the dynamics of a continuous
stochastic process. For a stochastic process taking values in a Riemannian
manifold, they have been studied extensively. We describe the Onsager-Machlup
functiona...
Welfare Analysis in Dynamic Models
August 24, 2019
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Statistics
Computer Science
Economics
Machine Learning
Machine Learning
Econometrics
This paper provides welfare metrics for dynamic choice. We give estimation
and inference methods for functions of the expected value of dynamic choice.
These parameters include average value by group, average derivatives with
respect to end...