Related papers: Heterogeneity dominates irreversibility in random …
Autoregressive language models achieve remarkable performance, yet a unified theory explaining their internal mechanisms, how training shapes representations, and why these representations support complex behavior remains incomplete. We…
We develop a generally applicable full-information inference method for heterogeneous agent models, combining aggregate time series data and repeated cross sections of micro data. To handle unobserved aggregate state variables that affect…
We study the convergence time to equilibrium of the Metropolis dynamics for the Generalized Random Energy Model with an arbitrary number of hierarchical levels, a finite and reversible continuous-time Markov process, in terms of the…
We propose a learning-based robust predictive control algorithm that compensates for significant uncertainty in the dynamics for a class of discrete-time systems that are nominally linear with an additive nonlinear component. Such systems…
Non-linear Hawkes processes with memory kernels given by the sum of Erlang kernels are considered. It is shown that their stability properties can be studied in terms of an associated class of piecewise deterministic Markov processes,…
We propose a probabilistic modeling framework for learning the dynamic patterns in the collective behaviors of social agents and developing profiles for different behavioral groups, using data collected from multiple information sources.…
Embedded random matrix ensembles are generic models for describing statistical properties of finite isolated interacting quantum many-particle systems. For the simplest spinless systems, with say $m$ particles in $N$ single particle states…
A new agent-based, bounded-confidence model for discrete one-dimensional opinion dynamics is presented. The agents interact if their opinions do not differ more than a tolerance parameter. In pairwise interactions, one of the pair, randomly…
Stochastic optimal control problems have a long tradition in applied probability, with the questions addressed being of high relevance in a multitude of fields. Even though theoretical solutions are well understood in many scenarios, their…
We introduce a generic class of dynamic nonlinear heterogeneous parameter models that incorporate individual and time fixed effects in both the intercept and slope. These models are subject to the incidental parameter problem, in that the…
We discuss recent results obtained for the Hamiltonian Mean Field model. The model describes a system of N fully-coupled particles in one dimension and shows a second-order phase transition from a clustered phase to a homogeneous one when…
In the field of ergodicity-breaking phases, it has been recognized that quantum avalanches can destabilize many-body localization at a wide range of disorder strengths. This has in particular been demonstrated by the numerical study of a…
Hierarchical Bayesian models are increasingly used in large, inhomogeneous complex network dynamical systems by modeling parameters as draws from a hyperparameter-governed distribution. However, theoretical guarantees for these estimates as…
The spectra of random feature matrices provide essential information on the conditioning of the linear system used in random feature regression problems and are thus connected to the consistency and generalization of random feature models.…
We study asymmetric rank-one spiked tensor models in the high-dimensional regime, where the noise entries are independent and identically distributed with zero mean, unit variance, and finite fourth moment. This extends the classical…
We propose a general method for the construction and analysis of unweighted $\epsilon$ - recurrence networks from chaotic time series. The selection of the critical threshold $\epsilon_c$ in our scheme is done empirically and we show that…
Longitudinal data are characterized by the dependence between observations coming from the same individual. In a regression perspective, such a dependence can be usefully ascribed to unobserved features (covariates) specific to each…
This paper characterizes the annealed, topological complexity (both of total critical points and of local minima) of the elastic manifold. This classical model of a disordered elastic system captures point configurations with…
Temporal coherence-persistent alignment across time-can arise between agents with fundamentally distinct dynamics, a behavior that classical diffusion models (e.g., Brownian motion, fractional Brownian motion, generalized Langevin equation)…
The design of reliable indicators to anticipate critical transitions in complex systems is an im portant task in order to detect a coming sudden regime shift and to take action in order to either prevent it or mitigate its consequences. We…