Related papers: Free Stein Irregularity and Dimension
Free probability and random matrix theory has shown to be a fruitful combination in many fields of research, such as digital communications, nuclear physics and mathematical finance. The link between free probability and eigenvalue…
Dynamical nature of the gauge degree of freedom and its effect to fermion spectrum are studied at $\beta=\infty$ for two-dimensional nonabelian chiral gauge theory in the vacuum overlap formulation. It is argue that the disordered gauge…
We examine the relation between the free volume per particle and the variance of the particle position, equivalent to a local Debye-Waller (DW) factor for a 2D glass-forming alloy using molecular dynamics simulations. We find that the…
We study a generalization of free Poisson random measure by replacing the intensity measure with a n.s.f. weight $\varphi$ on a von Neumann algebra $M$. We give an explicit construction of the free Poisson random weight using full Fock…
Suppose X is an n-tuple of selfadjoint elements in a tracial von Neumann algebra M. If z is a selfadjoint element in M and for some selfadjoint element y in the von Neumann algebra generated by X $\delta_0(y, z) < \delta_0(y) +…
Starting from the probability distribution of finite N-body systems, which maximises the Havrda--Charv\'at entropy, we build a Stein-type goodness-of-fit test. The Maxwell--Boltzmann distribution is exact only in the thermodynamic limit,…
Riemann's non-differentiable function is one of the most famous examples of continuous but nowhere differentiable functions, but it has also been shown to be relevant from a physical point of view. Indeed, it satisfies the Frisch-Parisi…
Around the mean dimensions and rate-distortion functions, using some tools from local entropy theory this paper establishes the following main results: $(1)$ We prove that for non-ergodic measures associated with almost sure processes, the…
Given a random variable $F$ regular enough in the sense of the Malliavin calculus, we are able to measure the distance between its law and almost any continuous probability law on the real line. The bounds are given in terms of the…
Let $X$ be a symmetric random matrix with independent but non-identically distributed centered Gaussian entries. We show that $$ \mathbf{E}\|X\|_{S_p} \asymp \mathbf{E}\Bigg[ \Bigg(\sum_i\Bigg(\sum_j X_{ij}^2\Bigg)^{p/2}\Bigg)^{1/p} \Bigg]…
The number of connected components can be remembered by the von Neumann algebra among Artin groups, the only possible exception being the case that corresponds to the free group factor problem. In the case of Coxeter groups, this result is…
The free analog of the pressure is introduced for multivariate noncommutative random variables and its Legendre transform is compared with Voiculescu's microstate free entropy.
Given a finite, directed, connected graph $\Gamma$ equipped with a weighting $\mu$ on its edges, we provide a construction of a von Neumann algebra equipped with a faithful, normal, positive linear functional…
The traditional Pi-theorem tells us that for any dimensionally invariant relation there exists a full set of independent dimensionless "Pi groups" which can be used to nondimensionalise the relation. In this paper, we seek to understand…
Uncertainty principle plays a crucial role in quantum mechanics, because it captures the essence of the inevitable randomness associated with the outcomes of two incompatible quantum measurements. Information entropy can perfectly describe…
We introduce the notion of proper proximality for finite von Neumann algebras, which naturally extends the notion of proper proximality for groups. Apart from the group von Neumann algebras of properly proximal groups, we provide a number…
We study the microstate free entropy of projections, and establish its basic properties similar to the self-adjoint variable case. Our main contribution is to characterize the pair-block freeness of projections by the additivity of their…
Building on recent work in statistical science, the paper presents a theory for modelling natural phenomena that unifies physical and statistical paradigms based on the underlying principle that a model must be nondimensionalizable. After…
In this article, we study the free vibration and the mechanical buckling of plates using a three dimensional consistent approach based on the scaled boundary finite element method. The in-plane dimensions of the plate are modeled by…
Degrees of freedom is a fundamental concept in statistical modeling, as it provides a quantitative description of the amount of fitting performed by a given procedure. But, despite this fundamental role in statistics, its behavior not…