Related papers: A Finite-State Gibbs Construction from a Recogniti…
Predictive inference requires balancing statistical accuracy against informational complexity, yet the choice of complexity measure is usually imposed rather than derived. We treat econometric objects as predictive rules, mappings from…
Zipf's law, and power laws in general, have attracted and continue to attract considerable attention in a wide variety of disciplines - from astronomy to demographics to software structure to economics to linguistics to zoology, and even…
We study maximum-entropy inference for finite-dimensional quantum states under linear moment constraints. Given expectation values of finitely many observables, the feasible set of states is convex but typically non-unique. The…
We study a rigidity problem for functions \(F:\R_{>0}\to\R_{\ge 0}\) that penalize deviation of a positive ratio from equilibrium \(x=1\). Assuming (i) a d'Alembert-type composition law on \(\R_{>0}\), and (ii) a single quadratic…
In this document, we aim to gather various results related to a compositional/categorical approach to rigorous Statistical Mechanics. Rigorous Statistical Mechanics is centered on the mathematical study of statistical systems. Central…
Gibbs' theorem, which is originally intended for canonical ensembles with complete statistics has been generalized to open systems with incomplete statistics. As a result of this generalization, it is shown that the stationary equilibrium…
We prove a priori estimates and, as sequel, existence of Euclidean Gibbs states for quantum lattice systems. For this purpose we develop a new analytical approach, the main tools of which are: first, a characterization of the Gibbs states…
We study Gibbs partition models, also known as composition schemes. Our main results comprehensively describe their phase diagram, including a phase transition from the convergent case described in Stufler (2018, Random Structures \&…
We develop a finite-data framework for certifying \emph{zero-defect} (neutral) configurations of positive vectors under the canonical separable reciprocal cost. We show that this scalar cost is characterized among non-constant continuous…
We propose a method to derive the stationary size distributions of a system, and the degree distributions of networks, using maximisation of the Gibbs-Shannon entropy. We apply this to a preferential attachment-type algorithm for systems of…
Limits of densities belonging to an exponential family appear in many applications, {e.g.} Gibbs models in Statistical Physics, relaxed combinatorial optimization, coding theory, critical likelihood computations, Bayes priors with singular…
Fundamental limits on the performance of feedback controllers are essential for benchmarking algorithms, guiding sensor selection, and certifying task feasibility -- yet few general-purpose tools exist for computing them. Existing…
The notion of entanglement has been useful for characterizing universal properties of quantum phases of matter. From the perspective of quantum information theory, it is tempting to ask whether their entanglement structures possess any…
We investigate the asymptotic behavior of the q-Racah probability measure on lozenge tilings of a hexagon whose side lengths scale linearly with a large parameter $L$, while the parameters $q\in(0,1)$ and $\kappa\in \mathbf{i}\mathbb{R}$…
The Gibbs distribution universally characterizes states of thermal equilibrium. In order to extend the Gibbs distribution to non-equilibrium steady states, one must relate the self-information $\mathcal{I}(x) = -\log(P_\text{ss}(x))$ of…
We consider the construction of a generalized Gibbs ensemble composed of complete bases of conserved charges in the repulsive Lieb-Liniger model. We will show that it is possible to construct these bases with varying locality as well as…
The Large Deviation Principle (LDP) and the Central Limit Theorem (CLT) are central pillars of probability theory. While their formulations are established under the i.i.d. assumption, the probabilistic foundation for power-law…
The study of a machine learning problem is in many ways is difficult to separate from the study of the loss function being used. One avenue of inquiry has been to look at these loss functions in terms of their properties as scoring rules…
We develop a class of non-life reserving models using a stable-1/2 random bridge to simulate the accumulation of paid claims, allowing for an essentially arbitrary choice of a priori distribution for the ultimate loss. Taking an…
We study the Gibbs statistics of high-density hard-core configurations on a unit square lattice $\mathbb{Z}^2$, for a general Euclidean exclusion distance $D$. As a by-product, we solve the disk-packing problem on $\mathbb{Z}^2$ for disks…