Related papers: Self-Similar Crossover in Statistical Physics
An algebraic approach is presented for the valuative interpolation problem, which recovers and generalizes prior characterizations known in the complex analytic setting by the authors. We use the asymptotic Samuel function to give the…
Simulations are valuable tools for empirically evaluating the properties of statistical methods and are primarily employed in methodological research to draw general conclusions about methods. In addition, they can often be useful to…
We show that, in spite of a rather common opinion, quantum mechanics can be represented as an approximation of classical statistical mechanics. The approximation under consideration is based on the ordinary Taylor expansion of physical…
In this article we propose a set of simple principles to guide empirical practice in synthetic control studies. The proposed principles follow from formal properties of synthetic control estimators, and pertain to the nature, implications,…
A closed mathematical model of the statistical self-gravitating system of scalar charged particles for conformal invariant scalar interactions is constructed on the basis of relativistic kinetics and gravitation theory. Asymptotic…
A continuous infinite system of point particles interacting via two-body strong superstable potential is considered in the framework of classical statistical mechanics. We define some kind of approximation of main quantities, which describe…
Self-normalized processes are basic to many probabilistic and statistical studies. They arise naturally in the the study of stochastic integrals, martingale inequalities and limit theorems, likelihood-based methods in hypothesis testing and…
An information-theoretic development is given for the problem of compound Poisson approximation, which parallels earlier treatments for Gaussian and Poisson approximation. Let $P_{S_n}$ be the distribution of a sum $S_n=\Sumn Y_i$ of…
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…
In this paper we consider asymptotic expansions for a class of sequences of symmetric functions of many variables. Applications to classical and free probability theory are discussed.
Symbolic approaches to the control design over complex systems employ the construction of finite-state models that are related to the original control systems, then use techniques from finite-state synthesis to compute controllers…
Higher criticism is a large-scale testing procedure that can attain the optimal detection boundary for sparse and faint signals. However, there has been a lack of knowledge in most existing works about its asymptotic distribution for more…
Estimation and inference procedures for synthetic control methods often do not allow for the existence of spillover effects, which are plausible in many applications. In this paper, we consider estimation and inference for synthetic control…
Quantitative properties of stochastic systems are usually specified in logics that allow one to compare the measure of executions satisfying certain temporal properties with thresholds. The model checking problem for stochastic systems with…
The transition structure of an automaton can be used to create a natural topology to the set of states of an automaton, generating, this way, a topological space. Probabilistic automata can also be modeled in terms of measure theory. A…
The aim of this review is to provide a concise overview of some of the generic approaches that have been developed to deal with the statistical description of large systems of interacting dissipative 'units'. The latter notion includes,…
Given an observable and its operator product expansion (OPE), we present expressions that carefully disentangle truncated sums of the perturbative series in powers of $\alpha$ from the non-perturbative (NP) corrections. This splitting is…
A basic statistical mechanics analysis of many-body systems with non-reciprocal pair interactions is presented. Different non-reciprocity classes in two- and three-dimensional binary systems (relevant to real experimental situations) are…
In this work we consider robust stabilization of uncertain dynamical systems and show that this can be achieved by solving a non-classically constrained analytic interpolation problem. In particular, this non-classical constraint confines…
Recently, symbolic regression (SR) has demonstrated its efficiency for discovering basic governing relations in physical systems. A major impact can be potentially achieved by coupling symbolic regression with asymptotic methodology. The…