Related papers: A new type of critical behaviour in random matrix …
We apply the fidelity metric approach to analyze two recently introduced models that exhibit a quantum phase transition to a topologically ordered phase. These quantum models have a known connection to classical statistical mechanical…
Why life persists at the edge of chaos is a question at the very heart of evolution. Here we show that molecules taking part in biochemical processes from small molecules to proteins are critical quantum mechanically. Electronic…
The effect of inclusion of higher-order interactions in the {\it XY} model on critical properties is studied by Monte Carlo simulations. It is found that an increasing number of the higher-order terms in the Hamiltonian modifies the shape…
Recent methods have been developed to map single-cell lineage statistics to population growth. Because population growth selects for exponentially rare phenotypes, these methods inherently depend on sampling large deviations from finite…
We set out to explore the possibility of investigating the critical behavior of systems with first-order phase transition using deep machine learning. We propose a machine learning protocol with ternary classification of instantaneous spin…
New advances in experiments on the random-field Ising model, as realized in dilute antiferromagnets, have brought us much closer to a full characterization of the static and dynamic critical behavior of the unusual phase transition in three…
An $n \times n$ matrix with $\pm 1$ entries which acts on $\mathbb{R}^n$ as a scaled isometry is called Hadamard. Such matrices exist in some, but not all dimensions. Combining number-theoretic and probabilistic tools we construct matrices…
Random non-commutative geometries are a novel approach to taking a non-perturbative path integral over geometries. They were introduced in arxiv.org/abs/1510.01377, where a first examination was performed. During this examination we found…
The class of random-cluster models is a unification of a variety of stochastic processes of significance for probability and statistical physics, including percolation, Ising, and Potts models; in addition, their study has impact on the…
We show how machine learning methods can unveil the fractional and delayed nature of discrete dynamical systems. In particular, we study the case of the fractional delayed logistic map. We show that given a trajectory, we can detect if it…
A new probability distribution to study lifetime data in reliability is introduced in this paper. This one is a first approach to a non-homogeneous phase-type distribution. It is built by considering one cut-point in the non-negative…
We study a continuous time branching process where an individual splits into two daughters with rate b and dies with rate a, starting from a single individual at t=0. We show that the model can be mapped exactly to a random walk problem…
Herding defines a deterministic dynamical system at the edge of chaos. It generates a sequence of model states and parameters by alternating parameter perturbations with state maximizations, where the sequence of states can be interpreted…
In classical probability theory, the term "cutoff" describes the property of some Markov chains to jump from (close to) their initial configuration to (close to) completely mixed in a very narrow window of time. We investigate how coherent…
We consider a stochastic process in which independent identically distributed random matrices are multiplied and where the Lyapunov exponent of the product is positive. We continue multiplying the random matrices as long as the norm,…
We study the boundary critical behavior of the three-dimensional Heisenberg universality class, in the presence of a bidimensional surface. By means of high-precision Monte Carlo simulations of an improved lattice model, where leading bulk…
We summarize some of the recent developments which link certain problems in combinatorial theory related to random growth to random matrix theory.
Classification and Regression Trees (CARTs) are off-the-shelf techniques in modern Statistics and Machine Learning. CARTs are traditionally built by means of a greedy procedure, sequentially deciding the splitting predictor variable(s) and…
Phase transitions generically occur in random matrix models as the parameters in the joint probability distribution of the random variables are varied. They affect all main features of the theory and the interpretation of statistical models…
Models of random walks are considered in which walkers are born at one location and die at all other locations with uniform death rate. Steady-state distributions of random walkers exhibit dimensionally dependent critical behavior as a…