Related papers: Scaling limits and aging for asymmetric trap model…

In this work, we analyze various scaling limits of the training dynamics of transformer models in the feature learning regime. We identify the set of parameterizations that admit well-defined infinite width and depth limits, allowing the…

Recent years have witnessed the surge of asynchronous parallel (async-parallel) iterative algorithms due to problems involving very large-scale data and a large number of decision variables. Because of asynchrony, the iterates are computed…

We define symmetric and asymmetric branching trees, a class of processes particularly suited for modeling genealogies of inhomogeneous populations where individuals may reproduce throughout life. In this framework, a broad class of…

We study the connections between volume growth, spectral properties and stochastic completeness of locally finite graphs. For a class of graphs with a very weak spherical symmetry we give a condition which implies both stochastic…

In random tiling and dimer models we can get various limit shapes which gives the boundaries between different types of phases. The shape fluctuations at these boundaries give rise to universal limit laws, in particular the Airy process. We…

Going from a scaling approach for birth/death processes, we investigate the scaling limit of solutions to non-Markovian stochastic control problems by studying the convergence of solutions to BSDEs driven a sequence of converging…

Using extensive molecular dynamics simulations, we have performed finite-size scaling (FSS) in the aging regime of a model glass-forming liquid to investigate how the length scales associated with amorphous order (static length) and dynamic…

Extended dynamical simulations have been performed on a 2+1 dimensional driven dimer lattice gas model to estimate ageing properties. The auto-correlation and the auto-response functions are determined and the corresponding scaling…

In this paper we propose a new model for volatility fluctuations in financial time series. This model relies on a non-stationary gaussian process that exhibits aging behavior. It turns out that its properties, over any finite time interval,…

Topological mapping of a large physical system on a graph, and its decomposition using universal measures is proposed. We find inherent limits to the potential for optimization of a given system and its approximate representations by…

We study the dynamics of the one dimensional disordered trap model presenting a broad distribution of trapping times $p(\tau) \sim 1/\tau^{1+\mu}$, when an external force is applied from the very beginning at $t=0$, or only after a waiting…

The ageing algebra is a local dynamical symmetry of many ageing systems, far from equilibrium, and with a dynamical exponent z=2. Here, new representations for an integer dynamical exponent z=n are constructed, which act non-locally on the…

Using Monte Carlo simulations, we have studied aging phenomena in three-dimensional Gaussian Ising spin-glass model focusing on quasi-equilibrium behavior of the spin auto-correlation functions. Weak violation of the time translational…

In this paper, we prove that if a sequence of electrical networks converges in the local Gromov-Hausdorff topology and satisfies a non-explosion condition, then the associated Bouchaud trap models (BTMs) also converge and exhibit aging.…

This paper considers limit theorems associated with subgraph counts in the age-dependent random connection model. First, we identify regimes where the count of sub-trees converges weakly to a stable random variable under suitable…

We derive the exact late-time asymptotics for small spherically symmetric solutions of nonlinear wave equations with a potential. The dominant tail is shown to result from the competition between linear and nonlinear effects.

We investigate some aspects of the ageing behavior observed in the contact process after a quench from its active phase to the critical point. In particular we discuss the scaling properties of the two-time response function and we…

In a recent paper (2024) M. Buratti and M.E:Muzychuck have established some lower bounds on the number of non isomorphic cyclic Steiner Triple Systems of order $v\equiv 1$ (mod $6$). We complete their result to the case $v\equiv 3$ (mod…

Aging has become the paradigm to describe dynamical behavior of glassy systems, and in particular spin glasses. Trap models have been introduced as simple caricatures of effective dynamics of such systems. In this Letter we show that in a…

We obtain sharp bounds for the number of n--cycles in a finite graph as a function of the number of edges, and prove that the complete graph is optimal in more ways than could be imagined. We prove sharp estimates on both the sum of k-th…