相关论文: Critical Gaussian Multiplicative Chaos revisited
We study linear chance-constrained problems where the coefficients follow a Gaussian mixture distribution. We provide mixed-binary quadratic programs that give inner and outer approximations of the chance constraint based on piecewise…
Lepage and Mackenzie have shown that tadpole renormalization and systematic improvement of lattice perturbation theory can lead to much improved numerical results in lattice gauge theory. It is shown that lattice perturbation theory using…
Quantized, compact graphs were shown to be excellent paradigms for quantum chaos in bounded systems. Connecting them with leads to infinity we show that they display all the features which characterize scattering systems with an underlying…
As an alternative to the well-known methods of "chaining" and "bracketing" that have been developed in the study of random fields, a new method, which is based on a {\em stochastic maximal inequality} derived by using the formula for…
Mandelbrot multiplicative cascades provide a construction of a dynamical system on a set of probability measures defined by inequalities on moments. To be more specific, beyond the first iteration, the trajectories take values in the set of…
We consider the imaginary Gaussian multiplicative chaos, i.e. the complex Wick exponential $\mu_\beta := :e^{i\beta \Gamma(x)}:$ for a log-correlated Gaussian field $\Gamma$ in $d \geq 1$ dimensions. We prove a basic density result, showing…
Gaussian Graphical Model selection problem is considered. Concentration graph is identified by multiple decision procedure based on individual tests. Optimal unbiased individual tests are constructed. It is shown that optimal tests are…
We show that for critical site percolation on the triangular lattice two new observables have conformally invariant scaling limits. In particular the expected number of clusters separating two pairs of points converges to an explicit…
For chaotic scattering on quantum graphs, the semiclassical approximation is exact. We use this fact and employ supersymmetry, the colour-flavour transformation, and the saddle-point approximation to calculate the exact expression for the…
Gaussian processes (GPs) with derivatives are useful in many applications, including Bayesian optimization, implicit surface reconstruction, and terrain reconstruction. Fitting a GP to function values and derivatives at $n$ points in $d$…
The martingale expansion provides a refined approximation to the marginal distributions of martingales beyond the normal approximation implied by the martingale central limit theorem. We develop a martingale expansion framework specifically…
In the spirit of [M. Biskup & O. Louidor, Adv. Math. 330 (2018)], we study the local structure of $\star$-scale invariant fields -- a class of log-correlated Gaussian fields -- around their extremal points by characterising the law of the…
Let $\alpha$ be a Steinhaus random multiplicative function. For a wide class of multiplicative functions $f$ we construct a multiplicative chaos measure arising from the Dirichlet series of $\alpha f$, in the whole $L^1$-regime. Our method…
1. Introduction 2. Massless QCD and Scale Invariance 3. The Renormalisation Group and Asymptotic Freedom 4. More on the Running Coupling 5. Application to Hard Processes 5.1 $R_{e^+e^-}$ and Related Processes 5.2 The Final State in $e^+e^-$…
This work is concerned with existence of weak solutions to discon- tinuous stochastic differential equations driven by multiplicative Gaus- sian noise and sliding mode control dynamics generated by stochastic differential equations with…
The transition from arbitrary to chaotic fluctuation properties in quantum systems is studied in a random matrix model. It is assumed that the Hamiltonian can be written as the sum of an arbitrary and a chaos producing part. The Gaussian…
We prove a CLT for spectra of submatrices of real symmetric and Hermitian Wigner matrices. We show that if in the standard normalization the fourth moment of the off-digonal entries is GOE/GUE-like then the limiting Gaussian process can be…
We examine the gravitational collapse of a non-linear sigma model in spherical symmetry. There exists a family of continuously self-similar solutions parameterized by the coupling constant of the theory. These solutions are calculated…
The spectral form factor of random matrix theory plays a key role in the description of disordered and chaotic quantum systems. While its moments are known to be approximately Gaussian, corrections subleading in the matrix dimension, $D$,…
This paper deals with Lata{\l}a's estimation of the moments of Gaussian chaoses. It is shown that his argument can be simplified significantly using Talagrand's generic chaining.