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We prove the emergence of stable fluctuations for reaction-diffusion in random environment with Weibull tails. This completes our work around the quenched to annealed transition phenomenon in this context of reaction diffusion. In [9], we…
In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast growing complex systems. In order to model such phenomena we apply both a discrete and a…
Using techniques of the theory of semigroups of linear operators we study the question of approximating solutions to equations governing diffusion in thin layers separated by a semi-permeable membrane. We show that as thickness of the…
The choice of boundary condition makes an essential difference in the solution structure of diffusion equations. The Dirichlet and Neumann boundary conditions and their combination have been the most used, but their legitimacy has been…
We analyse how simple local constraints in two dimensions lead a defect to exhibit robust, non-transient, and tunable, subdiffusion. We uncover a rich dynamical phenomenology realised in ice- and dimer-type models. On the microscopic scale…
Schr\"{o}dinger bridge can be viewed as a continuous-time stochastic control problem where the goal is to find an optimally controlled diffusion process whose terminal distribution coincides with a pre-specified target distribution. We…
Turbulent mixing and entrainment at the boundary of a cloud is studied by means of direct numerical simulations that couple the Eulerian description of the turbulent velocity and water vapor fields with a Lagrangian ensemble of cloud water…
The stochastic motion in a nonhomogeneous medium with traps is studied and diffusion properties of that system are discussed. The particle is subjected to a stochastic stimulation obeying a general L\'evy stable statistics and experiences…
Despite the remarkable empirical success of score-based diffusion models, their statistical guarantees remain underdeveloped. Existing analyses often provide pessimistic convergence rates that do not reflect the intrinsic low-dimensional…
The sensitivity of anomalous transport in crowded media to the form of the inter-particle interactions is investigated through computer simulations. We extend the highly simplified Lorentz model towards realistic natural systems by modeling…
We study a random process with reinforcement, which evolves following the dynamics of a given diffusion process in a bounded domain and is resampled according to its occupation measure when it reaches the boundary. We show that its…
Open-source software is a complex system; its development depends on the self-coordinated action of a large number of agents. This study follows the size of the building blocks, called "packages", of the Ubuntu Linux operating system over…
The stationary asymptotic properties of the diffusion limit of a multi-type branching process with neutral mutations are studied. For the critical and subcritical processes the interesting limits are those of quasi-stationary distributions…
Diffusion guidance is a powerful technique that enables controllable and high-fidelity sample generation with diffusion models. At a high level, it modifies the score function by incorporating a guidance term that steers the generative…
Diffusive transport of particles or, more generally, small objects is a ubiquitous feature of physical and chemical reaction systems. In configurations containing confining walls or constrictions transport is controlled both by the…
Light diffusion is usually associated with thick, opaque media. Indeed, multiple scattering is necessary for the onset of the diffusive regime and such condition is generally not met in almost transparent media. Nonetheless, at long enough…
We introduce a simple model of deterministic particles in weakly disordered media which exhibits a transition from normal to anomalous diffusion. The model consists of a set of non-interacting overdamped particles moving on a disordered…
We derive a general upper bound on the spreading rate of wavepackets in the framework of Schr\"odinger time evolution. Our result consists of showing that a portion of the wavepacket cannot escape outside a ball whose size grows dynamically…
Although an intimate relation between entropy and diffusion has been advocated for many years and even seems to have been verified in theory and experiments, a quantitatively reliable study, and any derivation of an algebraic relation…
Many approaches to modelling reaction-diffusion systems with anomalous transport rely on deterministic equations and ignore fluctuations arising due to finite particle numbers. Starting from an individual-based model we use a…