Related papers: A new type of critical behaviour in random matrix …
The notion of (auto) catalytic networks has become a cornerstone in understanding the possibility of a sudden dramatic increase of diversity in biological evolution as well as in the evolution of social and economical systems. Here we study…
We consider a branching-selection particle system on the real line. In this model the total size of the population at time $n$ is limited by $\exp\left(a n^{1/3}\right)$. At each step $n$, every individual dies while reproducing…
We derive the full phase diagram for a large family of two-parameter exponential random graph models, each containing a first order transition curve ending in a critical point.
Activated Random Walk is a system of interacting particles which presents a phase transition and a conjectured phenomenon of self-organized criticality. In this note, we prove that, in dimension 1, in the supercritical case, when a segment…
Motivated by understanding the phase structure of $d >1$ strings we investigate the $c=1$ matrix model with $g' (\tr M(t)^{2})^{2}$ interaction which is the simplest approximation of the model expected to describe the critical phenomena of…
In this paper we present a new classification model in machine learning. Our result is threefold: 1) The model produces comparable predictive accuracy to that of most common classification models. 2) It runs significantly faster than most…
We show, via explicit computation on a constrained bosonic model, that the presence of subsystem symmetries can lead to a quantum phase transition (QPT) where the critical point exhibits an emergent enhanced symmetry. Such a transition…
We discuss recent progress many problems in random matrix theory of a combinatorial nature, including several breakthroughs that solve long standing famous conjectures.
Quantum phase transitions are ubiquitous in quantum many body systems. The quantum fluctuations that occur at very low temperatures are known to be responsible for driving the system across different phases as a function of an external…
In this talk we go over several new developments regarding the techniques for a large class of non-hermitian matrix models with unitary randomness (complex random numbers). In particular, we discuss: (a) - A diagrammatic approach based on a…
Generative diffusion models have achieved spectacular performance in many areas of machine learning and generative modeling. While the fundamental ideas behind these models come from non-equilibrium physics, variational inference and…
The chiral phase transition in the conventional random matrix model is the second order in the chiral limit, irrespective of the number of flavors N_f, because it lacks the U_A(1)-breaking determinant interaction term. Furthermore, it…
The formation of topological defects in a second order phase transition in the early universe is an out-of-equilibrium process. Condensed matter experiments seem to support Zurek's mechanism, in which the freezing of thermal fluctuations…
This chapter describes the progress made during the past three decades in the finite size scaling analysis of the critical phenomena of the Anderson transition. The scaling theory of localisation and the Anderson model of localisation are…
The structure and design of optimal supply networks is an important topic in complex networks research. A fundamental trait of natural and man-made networks is the emergence of loops and the trade-off governing their formation: adding…
A particular class of random walks with a spin factor on a three dimensional cubic lattice is studied. This three dimensional random walk model is a simple generalization of random walk for the two dimensional Ising model. All critical…
We use the order complex corresponding to a symmetric matrix (defined by Giusti et al in 2015). In this note, we use it to define a class of models of random graphs, and show some surprising experimental results, showing sharp phase…
The link between a particular class of growth processes and random matrices was established in the now famous 1999 article of Baik, Deift, and Johansson on the length of the longest increasing subsequence of a random permutation. During the…
We use the Riemann-Hilbert approach, together with string and Toda equations, to study the topological expansion in the quartic random matrix model. The coefficients of the topological expansion are generating functions for the numbers…
First order phase transitions occur discretely from one state to another, however they often display continuous behavior. To understand this nature, it is essential to probe how the emergent phase nucleates, interacts and evolves with the…