Related papers: Counting Multiple Solutions in Glassy Random Matri…
The moment problem in probability theory asks for criteria for when there exists a unique measure with a given tuple of moments. We study a variant of this problem for random objects in a category, where a moment is given by the average…
Simple statistical agglomeration models can provide a universal link between the local structure and the glass transition temperature in network glasses. We first stress the physical features of the models and the hypothesis made, and then…
We study increasing subsequences (IS) for an ensemble of sequences given by permutation of numbers {1,2,...,n}. We consider a Boltzmann ensemble at temperature T. Thus each IS appears with the corresponding Boltzmann probability where the…
In these notes we introduce briefly the fundamentals of the replica method in the context of liquid theory and the structural glass problem. In particular, we explain and show its usefulness as a computation framework in the context of the…
We study the fluctuation problems at high temperature in the general mixed $p$-spin glass models under the weak external field assumption: $h= \rho N^{-\alpha}, \rho>0, \alpha \in [1/4,\infty]$. By extending the cluster expansion approach…
The richness of the mean-field solution of simple glasses leaves many of its features challenging to interpret. A minimal model that illuminates glass physics the same way the random energy model clarifies spin glass behavior would…
Let $P$ be a set of at most $n$ points and let $R$ be a set of at most $n$ geometric ranges, such as for example disks or rectangles, where each $p \in P$ has an associated supply $s_{p} > 0$, and each $r \in R$ has an associated demand…
Decays of unstable heavy particles usually involve the coherent sum of several amplitudes, like in a multiple slit experiment. Dedicated amplitude analysis techniques have been widely used to resolve these amplitudes for better…
Many inference problems involve inferring the number $N$ of components in some region, along with their properties $\{\mathbf{x}_i\}_{i=1}^N$, from a dataset $\mathcal{D}$. A common statistical example is finite mixture modelling. In the…
The present paper deals with the problem of improving the efficiency of large scale turbulent flow simulations. The high-fidelity methods for modelling turbulent flows become available for a wider range of applications thanks to the…
The quench dynamics of glassy systems are challenging. Due to aging, the system never reaches a stationary state but instead evolves on emergent scales that grow with its age. This slow evolution complicates field-theoretic descriptions, as…
We develop a parallel rejection algorithm to tackle the problem of low acceptance in Monte Carlo methods, and apply it to the simulation of the hopping conduction in Coulomb glasses using Graphics Processing Units, for which we also…
Cumulative probability models (CPMs) are a robust alternative to linear models for continuous outcomes. However, they are not feasible for very large datasets due to elevated running time and memory usage, which depend on the sample size,…
This work focuses on the construction of a new class of fourth-order accurate methods for multirate time evolution of systems of ordinary differential equations. We base our work on the Recursive Flux Splitting Multirate (RFSMR) version of…
We review 15 years of theoretical and experimental work on the non-linear response of glassy systems. We argue that an anomalous growth of the peak value of non-linear susceptibilities is a signature of growing "amorphous order" in the…
In molecular liquids such as water, time-delayed influences between microscopic or mesoscopic variables are typically probed using time-correlation functions, which are symmetric under detailed balance and therefore blind to dynamical…
We present a first principle scheme to compute the rigidity, i. e. the shear-modulus of structural glasses at finite temperatures using the cloned liquid theory, which combines the replica theory and the liquid theory. With the aid of the…
In this paper we expand our previous investigation of a quantum particle subject to the action of a random potential plus a fixed harmonic potential at a finite temperature T. In the classical limit the system reduces to a well-known…
The predictions of a class of phenomenological trap models of supercooled liquids are tested via computer simulation of a model glass-forming liquid. It is found that a model with a Gaussian distribution of trap energies provides a good…
Glass-forming liquids have been extensively studied in recent decades, but there is still no theory that fully describes these systems, and the diversity of treatments is in itself a barrier to understanding. Here we introduce a new simple…