Related papers: Magnificent Four
An integer partition of $n$ is a decreasing sequence of positive integers that add up to $[n]$. Back in $1979$ Macdonald posed a question about the limit value of the probability that two partitions chosen uniformly at random, and…
Extreme events play a crucial role in fluid turbulence. Inspired by methods from field theory, these extreme events, their evolution and probability can be computed with help of the instanton formalism as minimizers of a suitable action…
A precise characterization of structures occurring in turbulent fluid flows at high Reynolds numbers is one of the last open problems of classical physics. In this review we discuss recent developments related to the application of…
Large deviation theory and instanton calculus for stochastic systems are widely used to gain insight into the evolution and probability of rare events. At its core lies the realization that rare events are, under the right circumstances,…
We consider a Statistical Mechanics approach to granular systems by following the original ideas developed by Edwards. We use the concept of ``inherent states'', defined as the stable configurations in the potential energy landscape,…
We investigate the computational power of creating steady-states of quantum dissipative systems whose evolution is governed by time-independent and local couplings to a memoryless environment. We show that such a model allows for efficient…
Gibbs partition models are the largest class of infinite exchangeable partitions of the positive integers generalizing the product form of the probability function of the two-parameter Poisson-Dirichlet family. Recently those models have…
We present a novel algorithm for generating robust and consistent hypotheses for multiple-structure model fitting. Most of the existing methods utilize random sampling which produce varying results especially when outlier ratio is high. For…
Benford's Law predicts that the first significant digit on the leftmost side of numbers in real-life data is proportioned between all possible 1 to 9 digits approximately as in LOG(1 + 1/digit), so that low digits occur much more frequently…
Eigenvalue distributions are important dynamical quantities in matrix models, and it is an interesting challenge to study corresponding quantities in tensor models. We study real tensor eigenvalue/vector distributions for real symmetric…
Let $M^K_n$ be the moduli space of framed $K$-instantons with instanton number $n$ when $K$ is a compact simple Lie group of classical type. Due to Donaldson's theorem, its scheme structure is given by the regular locus of a GIT quotient of…
We investigate under which conditions a mixed state on a finite-dimensional multipartite quantum system may be the unique, globally stable fixed point of frustration-free semigroup dynamics subject to specified quasi-locality constraints.…
I carefully study noncommutative version of ADHM construction of instantons, which was proposed by Nekrasov and Schwarz. Noncommutative ${\bf R}^4$ is described as algebra of operators acting in Fock space. In ADHM construction of…
We introduce discrete time Markov chains that preserve uniform measures on boxed plane partitions. Elementary Markov steps change the size of the box from (a x b x c) to ((a-1) x (b+1) x c) or ((a+1) x (b-1) x c). Algorithmic realization of…
Plant differently colored points in the plane, then let random points ("Poisson rain") fall, and give each new point the color of the nearest existing point. Previous investigation and simulations strongly suggest that the colored regions…
We comment on some conceptual and and technical problems related to computational mechanics, point out some errors in several papers, and straighten out some wrong priority claims. We present explicitly the correct algorithm for…
Embedded random matrix ensembles are generic models for describing statistical properties of finite isolated interacting quantum many-particle systems. For the simplest spinless systems, with say $m$ particles in $N$ single particle states…
We investigate the differential geometry of the moduli space of instantons on S^3 x S^1. Extending previous results, we show that a sigma-model with this target space can be expected to possess a large N=4 superconformal symmetry,…
This paper derives a density matrix of the steady-state statistical mechanics compatible with the steady-state thermodynamics proposed by Oono and Paniconi [Prog. Theor. Phys. Suppl. {\bf 130}, 29 (1998)]. To this end, we adopt three…
We consider a two-dimensional point process whose points are separated into two disjoint components by a hard wall, and study the multivariate moment generating function of the corresponding disk counting statistics. We investigate the…