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We study the low temperature out of equilibrium Monte Carlo dynamics of the disordered Ising $p$-spin Model with $p=3$ and a small number of spin variables. We focus on sequences of configurations that are stable against single spin flips…
We review the ageing phenomenon in the context of simplest trap model, Bouchaud's REM-like trap model from a spectral theoretic point of view. We show that the generator of the dynamics of this model can be diagonalised exactly. Using this…
We give a general proof of aging for trap models using the arcsine law for stable subordinators. This proof is based on abstract conditions on the potential theory of the underlying graph and on the randomness of the trapping landscape. We…
Once the problem of ensemble averaging is removed, correlations between the response of a single molecule to an external driving field $F$, with the history of fluctuations of the particle, become detectable. Exact analytical theory for the…
This paper concerns the long-term behaviour of a system of interacting random walks labeled by vertices of a finite graph. The model is reversible which allows to use the method of electric networks in the study. In addition, examples of…
We consider dynamics of classical dimer models undergoing a phase transition to an ordered, frozen state. Relaxation processes are dominated by traps which are entropic in origin and can be traced to the locally jammed nature of the dimer…
We study the off-equilibrium dynamics of a particle in a general $N$-dimensional random potential when $N \to \infty$. We demonstrate the existence of two asymptotic time regimes: {\it i.} stationary dynamics, {\it ii.} slow aging dynamics…
Scaling laws describe how learning performance improves with data, compute, or training time, and have become a central theme in modern deep learning. We study this phenomenon in a canonical nonlinear model: phase retrieval with anisotropic…
We study the out of equilibrium dynamics of several models exhibiting aging. We attempt at identifying various types of aging systems using a phase space point of view: we introduce a trial classification, based on the overlap between two…
A one dimensional trap model for a thermally activated classical particle is introduced to simulate driven dynamics in presence of "ageing" effects. The depth of each trap increases with the time elapsed since the particle has fallen into…
In this paper we first provide several conditional limit theorems for L\'evy processes with negative drift and regularly varying tail. Then we apply them to study the asymptotic behavior of expectations of some exponential functionals of…
The current understanding of aging phenomena is mainly confined to the study of systems with short-ranged interactions. Little is known about the aging of long-ranged systems. Here, the aging in the phase-ordering kinetics of the…
The non-equilibrium dynamics of a one-dimensional Ising model with uniform, short-ranged three-spin interactions is investigated. It is shown that this model possesses an exponentially large number of metastable configurations that are…
We study the intermittent dynamics and the fluctuations of the dynamic correlation function of a simple aging system. Given its size $L$ and its coherence length $\xi$, the system can be divided into $N$ independent subsystems, where…
Although the title seems self-contradictory, it does not contain a misprint. The model we study is a seemingly minor modification of the "true self-avoiding walk" (TSAW) model of Amit, Parisi, and Peliti in two dimensions. The walks in it…
We consider a nearest neighbor random walk on the one-dimensional integer lattice with drift towards the origin determined by an asymptotically vanishing function of the number of visits to zero. We show the existence of distinct regimes…
Ageing phenomena are observed in a large variety of dynamical systems exhibiting a slow relaxation from a non-equilibrium initial state. Ageing can be characterised in terms of the linear response R(t,s) at time t to a local perturbation at…
We analyse the Langevin dynamics of the random walk, the scalar field, the X-Y model and the spinoidal decomposition. We study the deviations from the equilibrium dynamics theorems (FDT and homogeneity), the asymptotic behaviour of the…
Near a bifurcation point a system experiences critical slowing down. This leads to scaling behavior of fluctuations. We find that a periodically driven system may display three scaling regimes and scaling crossovers near a saddle-node…
The population loss of trained deep neural networks often follows precise power-law scaling relations with either the size of the training dataset or the number of parameters in the network. We propose a theory that explains the origins of…