Related papers: On Uniform Propagation of Chaos
This paper develops a theory of propagation of chaos for a system of weakly interacting particles whose terminal configuration is fixed as opposed to the initial configuration as customary. Such systems are modeled by backward stochastic…
Standard diffusion equation is based on Brownian motion of the dispersing species without considering persistence in the movement of the individuals. This description allows for the instantaneous spreading of the transported species over an…
We demonstrate that diffusively coupled limit-cycle oscillators on random networks can exhibit various complex dynamical patterns. Reducing the system to a network analog of the complex Ginzburg-Landau equation, we argue that uniform…
Biochemistry, ecology, and neuroscience are examples of prominent fields aiming at describing interacting systems that exhibit non-trivial couplings to complex, ever-changing environments. We have recently shown that linear interactions and…
We investigate the role of the noise schedule in diffusion processes on Lie groups, with particular emphasis on applications to lattice gauge theory. We show that a specific noise schedule leads to a linear decay of the expectation value of…
We study the limiting behaviour of the empirical measure of a system of diffusions interacting through their ranks when the number of diffusions tends to infinity. We prove that the limiting dynamics is given by a McKean-Vlasov evolution…
To better understand the inner workings of information spreading, network researchers often use simple models to capture the spreading dynamics. But most models only highlight the effect of local interactions on the global spreading of a…
We study an ensemble of random walkers carrying internal noisy phase oscillators which are synchronized among the walkers by local interactions. Due to individual mobility, the interaction partners of every walker change randomly, hereby…
We suggest an explanation of typical incubation times statistical features based on the universal behavior of exit times for diffusion models. We give a mathematically rigorous proof of the characteristic right skewness of the incubation…
Complex systems with global interactions tend to be stable if interactions between components are sufficiently homogeneous. In biological systems, which often have small copy numbers and interactions mediated by diffusing agents, noise and…
Denoising diffusion models, a class of generative models, have garnered immense interest lately in various deep-learning problems. A diffusion probabilistic model defines a forward diffusion stage where the input data is gradually perturbed…
In this work, we study the deterministic Cucker-Smale model with topological interaction. Focusing on the solutions of the corresponding Liouville equation, we show that propagation of chaos holds. Moreover, considering monokinetic…
Diffusion models for continuous data gained widespread adoption owing to their high quality generation and control mechanisms. However, controllable diffusion on discrete data faces challenges given that continuous guidance methods do not…
The rapidly increasing complexity of (mainly wireless) ad-hoc networks stresses the need of reliable distributed estimation of several variables of interest. The widely used centralized approach, in which the network nodes communicate their…
Nonlinear reaction-diffusion systems admit a wide variety of spatiotemporal patterns or structures. In this lecture, we point out that there is certain advantage in studying discrete arrays, namely cellular neural/nonlinear networks (CNNs),…
The concept of Turing instability, namely that diffusion can destabilize the uniform steady state, is well known either in the context of partial differential equations (PDEs) or in networks of dynamical systems. Recently reaction-diffusion…
Diffusion models, though originally designed for generative tasks, have demonstrated impressive self-supervised representation learning capabilities. A particularly intriguing phenomenon in these models is the emergence of unimodal…
Using equilibrium fluctuations to understand the response of a physical system to an externally imposed perturbation is the basis for linear response theory, which is widely used to interpret experiments and shed light on microscopic…
We identify a new type of pattern formation in spatially distributed active systems. We simulate one-dimensional two-component systems with predator-prey local interaction and pursuit-evasion taxis between the components. In a sufficiently…
We study the mean field Langevin dynamics and the associated particle system. By assuming the functional convexity of the energy, we obtain the $L^p$-convergence of the marginal distributions towards the unique invariant measure for the…