Related papers: Sharp threshold phenomena in statistical physics
This is the write-up of a set of lectures given at the Asia Europe Pacific School of High Energy Physics in Quy Nhon, Vietnam in September 2018, to an audience of PhD students in all branches of particle physics They cover the different…
These lectures provide an introduction to Soft-Collinear Effective Theory. As applications we discuss resummation for (i) soft-photon effects in QED, (ii) event-shape variables and (iii) jet cross sections.
We study a simple chemical reaction system and effects of the internal noise. The chemical reaction system causes the same transition phenomenon discussed by Togashi and Kaneko [Phys. Rev. Lett. 86 (2001) 2459; J. Phys. Soc. Jpn. 72 (2003)…
We investigate Takagi-type functions with roughness parameter $\gamma$ that are H\"older continuous with coefficient $H=\frac{\log\gamma}{\log \frac{1}{2}}.$ Analytical access is provided by an embedding into a dynamical system related to…
Global climate change, extreme climate events, earthquakes and their accompanying natural disasters pose significant risks to humanity. Yet due to the nonlinear feedbacks, strategic interactions and complex structure of the Earth system,…
We investigate collisional shifts of spectral lines involving excited hydrogenic states, where van der Waals coefficients have recently been shown to have large numerical values when expressed in atomic units. Particular emphasis is laid on…
The present-day nuclear structure theory exhibits a great degree of synergy with respect to methods that are used to describe various phenomena in heavy nuclear systems. From few-body methods, through the shell model to mean-field…
An account is given of the methods of working of Experimental High Energy Particle Physics, from the viewpoint of statisticians and others unfamiliar with the field. Current statistical problems, techniques, and hot topics are introduced…
This review concentrates on the specific properties and characteristics of damage structures generated with high-energy ions in the electronic energy loss regime. Irradiation experiments with so-called swift heavy ions (SHI) find…
For many Markov chains of practical interest, the invariant distribution is extremely sensitive to perturbations of some entries of the transition matrix, but insensitive to others; we give an example of such a chain, motivated by a problem…
A new formulation of statistical mechanics is put forward according to which a random variable characterizing a macroscopic body is postulated to be infinitely divisible. It leads to a parametric representation of partition function of an…
We study the asymptotic nature of geometric structures formed from a point cloud of observations of (generally heavy tailed) distributions in a Euclidean space of dimension greater than one. A typical example is given by the Betti numbers…
Autoregressive processes are intensively studied in statistics and other fields of applied stochastics. For many applications the overshoot and the threshold-time are of special interest. When the upward innovations are in the class of…
We consider the Stokes phenomenon for the solutions of some partial differential equations with variable coefficients in two complex variables, where initial data are holomorphic. We use the theory of (moment) summability and the theory of…
Proofs of sharp phase transition and noise sensitivity in percolation have been significantly simplified by the use of randomized algorithms, via the OSSS inequality (proved by O'Donnell, Saks, Schramm and Servedio (2005)) and the…
Transition phenomena between thermodynamic branch and turbulent branch in submarginal turbulent plasma are analyzed with statistical theory. Time-development of turbulent fluctuation is obtained by numerical simulations of Langevin equation…
We investigate the Coulomb phase shift, and derive and analyze new and more precise analytical formulae. We consider next to leading order terms to the Stirling approximation, and show that they are important at small values of the angular…
In this lecture, a limited introduction of gauge invariance in phase-space is provided, predicated on canonical transformations in quantum phase-space. Exact characteristic trajectories are also specified for the time-propagating Wigner…
Many features of physical systems, both qualitative and quantitative, become sharply defined or tractable only in some limiting situation. Examples are phase transitions in the thermodynamic limit, the emergence of classical mechanics from…
Noise plays a fundamental role in a wide variety of physical and biological dynamical systems. It can arise from an external forcing or due to random dynamics internal to the system. It is well established that even weak noise can result in…