Related papers: Phase transition in random tensors with multiple i…

We analyse how the sampling dynamics of distributions evolve in score-based diffusion models using cross-fluctuations, a centered-moment statistic from statistical physics. Specifically, we show that starting from an unbiased isotropic…

Compressed sensing deals with efficient recovery of analog signals from linear encodings. This paper presents a statistical study of compressed sensing by modeling the input signal as an i.i.d. process with known distribution. Three classes…

Parker Solar Probe (PSP) observes unexpectedly prevalent switchbacks, which are rapid magnetic field reversals that last from seconds to hours, in the inner heliosphere, posing new challenges to understanding their nature, origin, and…

We consider the thermodynamic behavior of local fluctuations occurring in a stable or metastable bulk phase. For a system with three or more phases, a simple analysis based on classical nucleation theory predicts that small fluctuations…

This work considers the notion of random tensors and reviews some fundamental concepts in statistics when applied to a tensor based data or signal. In several engineering fields such as Communications, Signal Processing, Machine learning,…

The microscopic model in which nodes interacting with each other are statistical systems is introduced. The nodes conditions are connected with a string of distinct microscopic configurations and depend on external parameters (pressure and…

Tensor ring (TR) decomposition is a simple but effective tensor network for analyzing and interpreting latent patterns of tensors. In this work, we propose a doubly randomized optimization framework for computing TR decomposition. It can be…

We use a recently proposed class of tensor-network states to study phase transitions in string-net models. These states encode the genuine features of the string-net condensate such as, e.g., a nontrivial perimeter law for Wilson loops…

The purpose of this paper is to initiate a phase theory for tensors under the Einstein product, and explore its applications in multilinear control systems. Firstly, the sectorial tensor decomposition for sectorial tensors is derived, which…

Accurate detection of signal components is a frequently-encountered challenge in statistical applications with low signal-to-noise ratio. This problem is particularly challenging in settings with heteroscedastic noise. In certain…

In this article, we develop methods for estimating a low rank tensor from noisy observations on a subset of its entries to achieve both statistical and computational efficiencies. There have been a lot of recent interests in this problem of…

Symmetry-protected topological (SPT) phases are short-range entangled quantum phases with symmetry, which have gapped excitations in the bulk and gapless modes at the edge. In this paper, we study the SPT phases in the spin-1 Heisenberg…

In a physical system, changing parameters such as temperature can induce a phase transition: an abrupt change from one state of matter to another. Analogous phenomena have recently been observed in large language models. Typically, the task…

Fabrication process variations can significantly influence the performance and yield of nano-scale electronic and photonic circuits. Stochastic spectral methods have achieved great success in quantifying the impact of process variations,…

We consider a threshold-crossing spiking process as a simple model for the activity within a population of neurons. Assuming that these neurons are driven by a common fluctuating input with Gaussian statistics, we evaluate the…

An Early modeling approach of transistors characterized by simplicity and accuracy in representing intrinsic non-linearities is applied to the characterization of propagation delay and level transition switching properties of NPN and PNP…

Noise-induced phase transitions are common in various complex systems, from physics to biology. In this article, we investigate the emergence of crucial events in noise-induced phase transition processes and their potential significance for…

This paper considers the problem of detecting equal-shaped non-overlapping unimodal peaks in the presence of Gaussian ergodic stationary noise, where the number, location and heights of the peaks are unknown. A multiple testing approach is…

A road map to understand the relation between the onset of the superconducting state with the particular optimum heterogeneity in granular superconductors is to study a Random Tranverse Ising Model on complex networks with a scale-free…

Systems composed of interacting self-propelled particles (SPPs) display different forms of order-disorder phase transitions relevant to collective motion. In this paper we propose a generalization of the Vicsek model characterized by an…