Related papers: Stochastic Stability: a Review and Some Perspectiv…
This paper deals a continuous-time state-dependent jump linear system, a particular kind of stochastic switching system. In particular, we consider a situation when the transition rate of the random jump process depends on the state…
Recent progress in approaches to determine the elastic constants of solids starting from the microscopic particle interactions is reviewed. On the theoretical side, density functional theory approaches are discussed and compared to more…
Understanding which system structure can sustain stable dynamics is a fundamental step in the design and analysis of large scale dynamical systems. Towards this goal, we investigate here the structural stability of systems with a random…
Survey article on representation stability and examples in algebraic geometry and topology, written for the Notices of the AMS.
A generalization of stable and casual stable probability distribution is proposed. The notion of $\go G$-casual stability can be used to introduce discrete analogues of stable distributions on the sent $\mathbb Z$ of integers. In contrary…
Gaussian Process State Space Models (GP-SSMs) are a non-parametric model class suitable to represent nonlinear dynamics. They become increasingly popular in data-driven modeling approaches, i.e. when no first-order physics-based models are…
For the dynamical glassy transition in the $p$-spin mean field spin glass model a thermodynamic description is given. The often considered marginal states are not the relevant ones for this purpose. This leads to consider a cooling…
This is essentially an expository note based on S. Paul's works on the stability of pairs. Its connection to K-stability will be also discussed.
This work primarily focuses on an operator inference methodology aimed at constructing low-dimensional dynamical models based on a priori hypotheses about their structure, often informed by established physics or expert insights. Stability…
Marginally stable solids have peculiar physical properties that were discovered and analyzed in the context of the jamming transition. We theoretically investigate the existence of marginal stability in a prototypical model for structural…
Due to the existence of multiple stationary distributions, we study the stability and instability of a stationary distribution for distribution dependent stochastic differential equations. This note is devoted to the instability of a…
In this paper we will investigate dynamic stability of percolation for the stochastic Ising model and the contact process. We also introduce the notion of downward and upward $\epsilon$-movability which will be a key tool for our analysis.
We study stable rationality properties of conic bundles over rational surfaces.
Stability guarantees have emerged as a principled way to evaluate feature attributions, but existing certification methods rely on heavily smoothed classifiers and often produce conservative guarantees. To address these limitations, we…
These lectures present results and problems on the characterization of structurally stable dynamics. We will shed light those which do not seem to depend on the regularity class (holomorphic or differentiable). Furthermore, we will present…
We briefly review the topic of AdS (in)stability, mainly focusing on a recently introduced analytic approach and its interplay with numerical results.
We formulate and prove a new criterion for stability of e-processes. It says that any e-process which is averagely bounded and concentrating is asymptotically stable. In the second part, we show how this general result applies to some shell…
Properties of Random Overlap Structures (ROSt)'s constructed from the Edwards-Anderson (EA) Spin Glass model on $\Z^d$ with periodic boundary conditions are studied. ROSt's are $\N\times\N$ random matrices whose entries are the overlaps of…
Simulations of a stochastic fixed-energy sandpile in one and two dimensions reveal slow relaxation of the order parameter, even far from the critical point. The decay of the activity is best described by a stretched-exponential form. The…
A popular method for selecting the number of clusters is based on stability arguments: one chooses the number of clusters such that the corresponding clustering results are "most stable". In recent years, a series of papers has analyzed the…