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"Distribution theory"
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A republic of equals : a manifesto for a just society
\"Political equality is the most basic tenet of democracy. Yet in America and other democratic nations, those with political power have special access to markets and public services. A Republic of Equals traces the massive income inequality observed in the United States and other rich democracies to politicized markets and avoidable gaps in opportunity-and explains why they are the root cause of what ails democracy today. In this provocative book, economist Jonathan Rothwell draws on the latest empirical evidence from across the social sciences to demonstrate how rich democracies have allowed racial politics and the interests of those at the top to subordinate justice. He looks at the rise of nationalism in Europe and the United States, revealing how this trend overlaps with racial prejudice and is related to mounting frustration with a political status quo that thrives on income inequality and inefficient markets. But economic differences are by no means inevitable. Differences in group status by race and ethnicity are dynamic and have reversed themselves across continents and within countries. Inequalities persist between races in the United States because Black Americans are denied equal access to markets and public services. Meanwhile, elite professional associations carve out privileged market status for their members, leading to compensation in excess of their skills. A Republic of Equals provides a bold new perspective on how to foster greater political and social equality, while moving societies closer to what a true republic should be.\"--Dust jacket.
Sums of Reciprocals of Fractional Parts and Multiplicative Diophantine Approximation
by
Velani, Sanju
,
Beresnevich, Victor
,
Haynes, Alan
in
Continued fractions
,
Diophantine analysis
,
Diophantine approximation
2020
There are two main interrelated goals of this paper. Firstly we investigate the sums
Overlapping Iterated Function Systems from the Perspective of Metric Number Theory
by
Baker, Simon
in
Diophantine approximation
,
Dynamical systems and ergodic theory -- Smooth dynamical systems: general theory -- Dimension theory of dynamical systems msc
,
Dynamics -- Mathematical models
2023
In this paper we develop a new approach for studying overlapping iterated function systems. This approach is inspired by a famous
result due to Khintchine from Diophantine approximation which shows that for a family of limsup sets, their Lebesgue measure is
determined by the convergence or divergence of naturally occurring volume sums. For many parameterised families of overlapping iterated
function systems, we prove that a typical member will exhibit similar Khintchine like behaviour. Families of iterated function systems
that our results apply to include those arising from Bernoulli convolutions, the
For each
Last of all, we introduce a property of an iterated function system that we call being consistently
separated with respect to a measure. We prove that this property implies that the pushforward of the measure is absolutely continuous.
We include several explicit examples of consistently separated iterated function systems.
Spectral expansions of non-self-adjoint generalized Laguerre semigroups
by
Savov, Mladen
,
Patie, Pierre
in
Laguerre polynomials
,
Nonselfadjoint operators
,
Spectral theory (Mathematics)
2021
We provide the spectral expansion in a weighted Hilbert space of a substantial class of invariant non-self-adjoint and non-local
Markov operators which appear in limit theorems for positive-valued Markov processes. We show that this class is in bijection with a
subset of negative definite functions and we name it the class of generalized Laguerre semigroups. Our approach, which goes beyond the
framework of perturbation theory, is based on an in-depth and original analysis of an intertwining relation that we establish between
this class and a self-adjoint Markov semigroup, whose spectral expansion is expressed in terms of the classical Laguerre polynomials. As
a by-product, we derive smoothness properties for the solution to the associated Cauchy problem as well as for the heat kernel. Our
methodology also reveals a variety of possible decays, including the hypocoercivity type phenomena, for the speed of convergence to
equilibrium for this class and enables us to provide an interpretation of these in terms of the rate of growth of the weighted Hilbert
space norms of the spectral projections. Depending on the analytic properties of the aforementioned negative definite functions, we are
led to implement several strategies, which require new developments in a variety of contexts, to derive precise upper bounds for these
norms.
Mixtures : estimation and applications
by
Mengersen, Kerrie L.
,
Robert, Christian P.
,
Titterington, D. M. (David Michael)
in
Distribution (Probability theory)
,
Mixture distributions (Probability theory)
2011
This book uses the EM (expectation maximization) algorithm to simultaneously estimate the missing data and unknown parameter(s) associated with a data set.The parameters describe the component distributions of the mixture; the distributions may be continuous or discrete.
Global justice and finance
\"Can global justice be promoted by distributing money more equitably? This book casts new light on this question by considering what is presupposed about finance, and challenges the tradition of global justice theory that proposes modest reforms to the international institutional order as sufficient for achieving a more just world\"-- Provided by publisher.
The coming of neo feudalism : a warning to the global middle class
by
Kotkin, Joel
in
Distribution (Economic theory) -- History -- 21st century
,
Social classes -- History -- 21st century
,
Social history -- 21st century
2020
Following a remarkable epoch of greater dispersion of wealth and opportunity, we are inexorably returning towards a more feudal era marked by greater concentration of wealth and property, reduced upward mobility, demographic stagnation, and increased dogmatism. If the last seventy years saw a massive expansion of the middle class, not only in America but in much of the developed world, today that class is declining and a new, more hierarchical society is emerging.The new class structure resembles that of Medieval times. At the apex of the new order are two classes-a reborn clerical elite, the clerisy, which dominates the upper part of the professional ranks, universities, media and culture, and a new aristocracy led by tech oligarchs with unprecedented wealth and growing control of information. These two classes correspond to the old French First and Second Estates.Below these two classes lies what was once called the Third Estate. This includes the yeomanry, which is made up largely of small businesspeople, minor property owners, skilled workers and private-sector oriented professionals. Ascendant for much of modern history, this class is in decline while those below them, the new Serfs, grow in numbers-a vast, expanding property-less population.The trends are mounting, but we can still reverse them-if people understand what is actually occurring and have the capability to oppose them.