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Data processing for the sandwiched Rényi divergence: a condition for equality
(SpringerLetters in Mathematical Physics, 2016)
The $\alpha$-sandwiched Rényi divergence satisfies the data processing inequality, i.e. monotonicity under quantum operations, for $\alpha$ $\geq$ 1/2. In this article, we derive a necessary and sufficient algebraic condition ...
Asymptotics of Partial Density Functions for Divisors
(SpringerThe Journal of Geometric Analysis, 2016-09-19)
We study the asymptotic behaviour of the partial density function associated to sections of a positive hermitian line bundle that vanish to a particular order along a fixed divisor $Y$ . Assuming the data in question is ...
Non-Backtracking Loop Soups and Statistical Mechanics on Spin Networks
(SpringerAnnales Henri Poincaré, 2016-10-20)
We introduce and study a Markov field on the edges of a graph $\mathcal{G}$ in dimension $\textit{d}$ ≥ 2 whose configurations are spin networks. The field arises naturally as the edge-occupation field of a Poissonian model ...
Unstable mode solutions to the Klein-Gordon equation in Kerr-anti-de Sitter spacetimes
(SpringerCommunications in Mathematical Physics, 2016)
For any cosmological constant Λ = −3/$l^2$ < 0 and any $\alpha$ < 9/4, we find a Kerr-AdS spacetime ($M$, $g_{KAdS}$), in which the Klein-Gordon equation $\square g_{KAdS}$ ψ+$\alpha$/$l^2$ψ = 0 has an exponentially growing ...
Homogeneous Monge-Amp$\grave e$re Equations and Canonical Tubular Neighbourhoods in Kähler Geometry
(Oxford University PressInternational Mathematics Research Notices, 2016)
We prove the existence of canonical tubular neighbourhoods around complex submanifolds of Kähler manifolds that are adapted to both the holomorphic and symplectic structure. This is done by solving the complex Homogeneous ...
Acylindrical Hyperbolicity, non-simplicity and SQ-universality of groups splitting over $\mathbb{Z}$
(De GruyterJournal of Group Theory, 2016-09-15)
We show, using acylindrical hyperbolicity, that a finitely generated group splitting over $\mathbb{Z}$ cannot be simple. We also obtain SQ-universality in most cases, for instance a balanced group (one where if two powers ...
Bulk eigenvalue statistics for random regular graphs
(Institute of Mathematical StatisticsAnnals of Probability, 2016)
We consider the uniform random d-regular graph on N vertices, with d ∈ [N$^{\alpha}$,N$^{2/3−\alpha}$] for arbitrary α > 0. We prove that in the bulk of the spectrum the local eigenvalue correlation
functions and the ...
Uniform Bounds for Black--Scholes Implied Volatility
(Society for Industrial and Applied MathematicsSIAM Journal on Financial Mathematics, 2016-11-29)
In this note, Black--Scholes implied volatility is expressed in terms of various optimization problems. From these representations, upper and lower bounds are derived which hold uniformly across moneyness and call price. ...
On the number of non-zero elements of joint degree vectors
(Electronic Journal of CombinatoricsThe Electronic Journal of Combinatorics, 2017-03-31)
Joint degree vectors give the number of edges between vertices of degree i and degree j for 1 ≤ i ≤ j ≤ n-1 in an n-vertex graph. We find lower and upper bounds for the maximum number of nonzero elements in a joint degree ...
A Liouville hyperbolic souvlaki
(Institute of Mathematical StatisticsElectronic Journal of Probability, 2017-04-25)
We construct a transient bounded-degree graph no transient subgraph of which embeds in any surface of finite genus.
Moreover, we construct a transient, Liouville, bounded-degree, Gromov–hyperbolic graph with trivial ...