Related papers: The Effective Bootstrap
Current numerical conformal bootstrap techniques carve out islands in theory space by repeatedly checking whether points are allowed or excluded. We propose a new method for searching theory space that replaces the binary information…
In critical lattice models, distance ($r$) dependent correlation functions contain power laws $r^{-2\Delta}$ governed by scaling dimensions $\Delta$ of an underlying continuum field theory. In Monte Carlo simulations, the leading dimensions…
We provide an effective solution of the 1D crossing equation. We begin by arguing that crossing constraints can be recast in terms of bases of sum rules associated to special sets of CFT data -- extremal solutions -- which solve these…
The critical $O(N)$ CFT in spacetime dimensions $2 < d < 4$ is one of the most important examples of a conformal field theory, with the Ising CFT at $N=1$, $2 \leq d < 4$, as a notable special case. Apart from numerous physical…
We introduce a stochastic version of the cutting-plane method for a large class of data-driven Mixed-Integer Nonlinear Optimization (MINLO) problems. We show that under very weak assumptions the stochastic algorithm is able to converge to…
Bootstrapping can produce confidence levels for hypotheses about quadratic regression models - such as whether the U-shape is inverted, and the location of optima. The method has several advantages over conventional methods: it provides…
We propose the relaxation bootstrap method for the numerical solution of multi-matrix models in the large $N$ limit, developing and improving the recent proposal of H.Lin. It gives rigorous inequalities on the single trace moments of the…
We provide new theoretical results in the field of inverse regression methods for dimension reduction. Our approach is based on the study of some empirical processes that lie close to a certain dimension reduction subspace, called the…
Regression problems with bounded continuous outcomes frequently arise in real-world statistical and machine learning applications, such as the analysis of rates and proportions. A central challenge in this setting is predicting a response…
We develop and implement a novel fast bootstrap for dependent data. Our scheme is based on the i.i.d. resampling of the smoothed moment indicators. We characterize the class of parametric and semi-parametric estimation problems for which…
We introduce PyCFTBoot, a wrapper designed to reduce the barrier to entry in conformal bootstrap calculations that require semidefinite programming. Symengine and SDPB are used for the most intensive symbolic and numerical steps…
We apply analytic conformal bootstrap ideas in Mellin space to conformal field theories with $O(N)$ symmetry and cubic anisotropy. We write down the conditions arising from the consistency between the operator product expansion and crossing…
In this paper, we investigate the (in)-consistency of different bootstrap methods for constructing confidence intervals in the class of estimators that converge at rate $n^{1/3}$. The Grenander estimator, the nonparametric maximum…
There are some papers which describe the use of bootstrap techniques in point process statistics. The aim of the present paper is to show that the form in which bootstrap is used there is dubious. In case of variance estimation of pair…
A program of wide interest in modern conformal bootstrap studies is to numerically solve general conformal field theories, based on a critical assumption that the dynamics is encoded in the conformal four-point crossing equations and…
In this paper, we examine the validity of non-parametric spatial bootstrap as a procedure to quantify errors in estimates of N-point correlation functions. We do this by means of a small simulation study with simple point process models and…
Using numerical bootstrap method, we determine the critical exponents of the minimal three-dimensional $\mathcal{N}=1$ superconformal field theory (SCFT) to be $\eta_{\sigma}=0.168888(60)$ and $\omega=0.882(9)$. The model was argued in…
The analytic conformal bootstrap is an array of techniques to characterize, constrain, and solve strongly interacting quantum field theories using symmetries, causality, unitarity, and other general principles. In the last decade, bolstered…
In decision making problems for continuous state and action spaces, linear dynamical models are widely employed. Specifically, policies for stochastic linear systems subject to quadratic cost functions capture a large number of applications…
We present a new algorithm for the numerical evaluation of five-point conformal blocks in $d$-dimensions, greatly improving the efficiency of their computation. To do this we use an appropriate ansatz for the blocks as a series expansion in…