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Gaussian tree constraints applied to acoustic linguistic functional data
(ElsevierJournal of Multivariate Analysis, 2016-10-11)
Evolutionary models of languages are usually considered to take the form of trees. With the development of so-called tree constraints the plausibility of the tree model assumptions can be assessed by checking whether the ...
Computations in monotone Floer theory
(Department of Pure Mathematics and Mathematical Statistics, University of CambridgeUniversity of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 2016-06-28)
Floer theory is a rich collection of tools for studying symplectic manifolds and their Lagrangian submanifolds with the help of holomorphic curves. Its origins lie in estimating the numbers of equilibria in Hamiltonian ...
Spectral gap in the group of affine transformations over prime fields
(University of ToulouseAnnales de la Faculte des Sciences de Toulousehttp://afst.cedram.org/item?id=AFST_2016_6_25_5_969_0, 2016-11-01)
We study random walks on the groups $\Bbb F^d_p \rtimes$ SL$_d$($\Bbb F_p$). We estimate the spectral gap in terms of the spectral gap of the projection to the linear part SL$_d$($\Bbb F_p$). This problem is motivated by ...
INVARIANT DISTRIBUTIONS AND THE GEODESIC RAY TRANSFORM
(Mathematical Science PublishersAnalysis & PDE, 2016-12-11)
We establish an equivalence principle between the solenoidal injectivity of the geodesic ray transform acting on symmetric $\textit{m}$-tensors and the existence of invariant distributions or smooth first integrals with ...
Exploring Random Geometry with the Gaussian Free Field
(University of CambridgeDPMMSPeterhouse, 2016-10-01)
This thesis studies the geometry of objects from 2-dimensional statistical physics in the continuum.
Chapter 1 is an introduction to Schramm-Loewner evolutions (SLE). SLEs are the canonical family of non-self-intersecting, ...
Pairwise Markov properties for regression graphs
(WileyStat, 2016-11-13)
With a sequence of regressions, one may generate joint probability distributions. One starts with a joint, marginal distribution of context variables having possibly a concentration graph structure and continues with an ...
Statistical and computational trade-offs in estimation of sparse principal components
(Institute of Mathematical StatisticsAnnals of Statistics, 2016)
In recent years, Sparse Principal Component Analysis has emerged as an extremely popular dimension reduction technique for highdimensional data. The theoretical challenge, in the simplest case, is to estimate the leading ...
Deformations of Cayley submanifolds
(University of CambridgeDepartment of Pure Mathematics and Mathematical StatisticsTrinity College, 2016-03-01)
Cayley submanifolds of R^8 were introduced by Harvey and Lawson as an instance of calibrated submanifolds, extending the volume-minimising properties of complex submanifolds in Kähler manifolds. More generally, Cayley ...
Level-raising and symmetric power functoriality, III
(Duke University PressDuke Mathematical Journal, 2016-12-09)
The simplest case of the Langlands functoriality principle asserts the existence of
the symmetric powers Symn of a cuspidal representation of GL.2/ over the adèles of
F , where F is a number field. In 1978, Gelbart and ...
A 2-adic automorphy lifting theorem for unitary groups over CM fields
(SpringerMathematische Zeitschrift, 2016)
We prove a ‘minimal’ type automorphy lifting theorem for 2-adic Galois representations of unitary type, over imaginary CM fields. We use this to improve an automorphy lifting theorem of Kisin for GL_2.