Related papers: Dynamical Invariants from Asymptotic Composants
The dilaton is a possible inflaton candidate following recent CMB data allowing a non-minimal coupling to the Ricci curvature scalar in the early Universe. In this paper, we introduce an approach that has seldom been used in the literature,…
One of the fundamental questions in inflation is how to characterize the structure of different types of models in the field theoretic landscape. Proposals in this direction include attempts to directly characterize the formal structure of…
We describe the structure of the asymptotic lines near an inflection point of a Lagrangean surface, proving that in the generic situation it corresponds to two of the three possible cases when the discriminant curve has a cusp singularity.…
The decoherence of quantum fluctuations into classical perturbations during inflation is discussed. A simple quantum mechanical argument, using a spatial particle wavefunction rather than a field description, shows that observable…
The convergence of simultaneous and marginal predictive classifiers under partition exchangeability in supervised classification is obtained. The result shows the asymptotic convergence of these classifiers under infinite amount of training…
We compute correlation functions of the primordial density perturbations when they couple to a gapless, strongly coupled sector of spectator fields -- ``unparticles" -- during inflation. We first derive a four-point function of conformally…
Asymptotic couplings by reflection are constructed for a class of non-linear monotone SPDES (stochastic partial differential equations). As applications, the gradient/H\"older estimates as well as the exponential convergence are derived for…
We investigate the small-mass asymptotics of a class of massive $d$ dimensional angular integrals. These integrals arise in a wide range of perturbative quantum field theory calculations. We derive expressions characterizing their behavior…
In this thesis, we consider domino tilings of three-dimensional regions, especially those of the form $\mathcal{D} \times [0,N]$. In particular, we investigate the connected components of the space of tilings of such regions by flips, the…
The systematic diagnosis of band topology enabled by the method of "symmetry indicators" underlies the recent advances in the search for new materials realizing topological crystalline insulators. Such an efficient method has been missing…
Some new results on geometry of classical parabolic Monge-Amp\`ere equations (PMA) are presented. PMAs are either \emph{integrable}, or \emph{nonintegrable} according to integrability of its characteristic distribution. All integrable PMAs…
The symmetry-based indicator [H. C. Po, A. Vishwanath, H. Watanabe, Nat. Commun. 8, 50 (2017)] is a practical tool to diagnose topological materials in the band theory. In this note, we present two directions to generalize the…
To gain insight into the mechanisms behind machine learning methods, it is crucial to establish connections among the features describing data points. However, these correlations often exhibit a high-dimensional and strongly nonlinear…
We investigate the effects of large inhomogeneities in both the inflaton field and its momentum. We find that in general, large kinetic perturbations reduce the number of e-folds of inflation. In particular, we observe that inflationary…
We construct an asymptotic approximation to the solution of a transmission problem for a body containing a region occupied by many small inclusions. The cluster of inclusions is characterised by two small parameters that determine the…
This paper introduces an inner product on chain complexes of finite simplicial complexes that is well-adapted to the harmonic study of subdivisions. Its definition utilizes a decomposition of the chain spaces that suggests a sequence of…
Symmetries play an essential role in identifying and characterizing topological states of matter. Here, we classify topologically two-dimensional (2D) insulators and semimetals with vanishing spin-orbit coupling using time-reversal…
We consider several aspects of conjugating symmetry methods, including the method of invariants, with an asymptotic approach. In particular we consider how to extend to the stochastic setting several ideas which are well established in the…
We illustrate how the notion of asymptotic coupling provides a flexible and intuitive framework for proving the uniqueness of invariant measures for a variety of stochastic partial differential equations whose deterministic counterpart…
Singular statistical models arise whenever different parameter values induce the same distribution, leading to non-identifiability and a breakdown of classical asymptotic theory. While existing approaches analyze these phenomena in…