Related papers: Spin Glass Concepts in Computer Science, Statistic…
The study of spin-glass dynamics, long considered the paradigmatic complex system, has reached important milestones. The availability of single crystals has allowed the experimental measurement of spin-glass coherence lengths of almost…
Spin glasses are models of statistical mechanics in which a large number of simple elements interact with one another in a disordered fashion. One of the fundamental results of the theory is the Parisi formula, which identifies the limit of…
The Hopfield model, originally inspired by spin-glass physics, occupies a central place at the intersection of statistical mechanics, neural networks, and modern artificial intelligence. Despite its conceptual simplicity and broad…
Spin glasses are the paradigm of complex systems. These materials present really slow dynamics. However, the nature of the spin glass phase in finite dimensional systems is still controversial. Different theories describing the low…
Marginal optima are minima or maxima of a function with many nearly flat directions. In settings with many competing optima, marginal ones tend to attract algorithms and physical dynamics. Often, the important family of marginal attractors…
Glassy behavior is one of the main open problems in condensed matter physics. In this thesis, we approach the problem by studying spin-glasses and colloids, using several complementary strategies. From the point of view of model building,…
Numerical studies in random systems are plagued with strong finite-size effects and boundary effects. We introduce a window-measurement method as a practical solution to these difficulties. We observe physical quantities only within a…
If we have a system of binary variables and we measure the pairwise correlations among these variables, then the least structured or maximum entropy model for their joint distribution is an Ising model with pairwise interactions among the…
Submodular functions are discrete functions that model laws of diminishing returns and enjoy numerous algorithmic applications. They have been used in many areas, including combinatorial optimization, machine learning, and economics. In…
These lecture notes introduce some topics of classical statistical physics, particularly those that are relevant for neural networks and deep learning. Statistical physics is treated as a branch of probability theory or statistics, with the…
We revisit the concept of marginal stability in glasses, and determine its range of applicability in the context of avalanche-type response to slow external driving. We argue that there is an intimate connection between a pseudo-gap in the…
We introduce efficient algorithms for approximate sampling from symmetric Gibbs distributions on the sparse random (hyper)graph. The examples we consider include (but are not restricted to) important distributions on spin systems and…
This talk describes how techniques developed by Computer Scientists have helped our understanding of certain problems in statistical physics which involve randomness and ``frustration''. Examples will be given from two problems that have…
The central object of this PhD thesis is known under different names in the fields of computer science and statistical mechanics. In computer science, it is called the Maximum Cut problem, one of the famous twenty-one Karp's original…
Spin glasses occupy a unique place in condensed matter: they freeze collectively while remaining struc-turally disordered, and they exhibit slow, history-dependent dynamics that reflect an exceptionally rug-ged free-energy landscape. This…
High-dimensional random landscapes underlie phenomena as diverse as glassy physics and optimization in machine learning, and even their simplest toy models already display extraordinarily rich behavior. This thesis aims to deepen our…
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…
This review presents various aspects of a mean-field spin glass model known as the p-spin spherical spin glass model, which has raised a lot of interest in the study of spin glasses, and also for its possible links with a mean-field theory…
We have studied the diluted Heisenberg spin glass model in a 3-component random field for the commonly-used one-dimensional long-range model where the probability that two spins separated by a distance $r$ interact with one another falls as…
Finding minima of a real valued non-convex function over a high dimensional space is a major challenge in science. We provide evidence that some such functions that are defined on high dimensional domains have a narrow band of values whose…