Related papers: Critical perturbation in standard map: A better ap…
A rare decay $K_L \to \mu^+ \mu^- $ has been measured precisely, while a rare decay $K_S \to \mu^+ \mu^- $ will be observed by an upgrade of the LHCb experiment. Although both processes are almost CP-conserving decays, we point out that an…
We bring together three key amplification mechanisms in linear dynamical systems: spectral criticality, resonance, and non-normality. We present a unified linear framework that both distinguishes and quantitatively links these effects…
Considering a Markov chain defined on a cycle, near-quadratic improvement of mixing is shown when only a subtle perturbation is introduced to the structure and non-reversible transition probabilities are used. More precisely, a mixing time…
The methods of conformal field theory are used to compute the crossing probabilities between segments of the boundary of a compact two-dimensional region at the percolation threshold. These probabilities are shown to be invariant not only…
Statistical systems near a classical critical point have been intensively studied both from theoretical and experimental points of view. In particular, correlation functions are of relevance in comparing theoretical models with the…
The CP conserving amplitudes for the decays $K\to3\pi$ are calculated in Chiral Perturbation Theory. The calculation is made at the next-to-leading order including strong and local electromagnetic isospin breaking. A comparison is made…
The basic question in perturbation analysis of Markov chains is: how do small changes in the transition kernels of Markov chains translate to chains in their stationary distributions? Many papers on the subject have shown, roughly, that the…
The first lattice result from the RBC and UKQCD Collaborations and improved perturbative calculations of $\varepsilon^{\prime}_K / \varepsilon_K$ have implied that the Standard-Model (SM) expectation deviates from measured values at the…
We present an updated analysis of the rare decay $K_{L}\to\pi^{0}\mu^{+}\mu^{-}$ within the Standard Model. In particular, we present the first complete calculation of the two-photon CP-conserving amplitude within Chiral Perturbation…
We review the Standard Model predictions of CP violation in kaon decays. We present an elementary introduction to Chiral Perturbation Theory, four--quark effective hamiltonians and the relation among them. Particular attention is devoted to…
Matrix perturbation bounds (such as Weyl and Davis-Kahan) are used abundantly in many areas of mathematics and data science. Many bounds (such as the above two) involve the spectral norm of the noise matrix and are sharp in worst case…
$K\pi$ scattering and $K_{\mu 4}$ decays are studied at leading order of improved chiral perturbation theory. It is shown that high precision $K_{\mu 4}$ experiments at, e.g., DA$\Phi$NE should allow for a direct measurement of the quark…
We investigate the stability of quantum Markov processes with respect to perturbations of their transition maps. In the first part, we introduce a condition number that measures the sensitivity of fixed points of a quantum channel to…
The perturbation theory for critical points of causal variational principles is developed. We first analyze the class of perturbations obtained by multiplying the universal measure by a weight function and taking the push-forward under a…
Critical transitions occur in a variety of dynamical systems. Here, we employ quantifiers of chaos to identify changes in the dynamical structure of complex systems preceding critical transitions. As suitable indicator variables for…
Calibration, the practice of choosing the parameters of a structural model to match certain empirical moments, can be viewed as minimum distance estimation. Existing standard error formulas for such estimators require a consistent estimate…
For piecewise expanding one-dimensional maps without periodic turning points we prove that isolated eigenvalues of small (random) perturbations of these maps are close to isolated eigenvalues of the unperturbed system. (Here ``eigenvalue''…
We calculate the ratios R_{e/mu}^{(P)} = Gamma(P -> e nu)/Gamma (P -> mu nu) (P=pi,K) in Chiral Perturbation Theory to order e^2 p^4. We complement the one- and two-loop effective theory results with a matching calculation of the local…
In this paper we study random linear systems with $k$ variables per equation over the finite field GF(2), or equivalently $k$-XOR-CNF formulas. In a previous paper Creignou and Daud\'e proved that the phase transition for the consistency…
The rare $K \to \pi \nu \bar{\nu}$ decay modes and the parameter $\epsilon_K$ that measures CP violation in Kaon mixing are sensitive probes of physics beyond the standard model. In this article we provide the updated standard-model…