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We consider a family of models having an arbitrary positive amount of mass on each site and randomly exchanging an arbitrary amount of mass with nearest neighbor sites. We restrict to the case of diffusive models. We identify a class of…
We study a networked system of innovation processes, where each process is modeled as an urn with infinitely many colors-a classical framework for capturing the emergence of novelties. Extending this paradigm, we analyze a model of…
We analytically compute the full counting statistics of charge transfer in a classical automaton of interacting charged particles. Deriving a closed-form expression for the moment generating function with respect to a stationary equilibrium…
General equilibrium equations in economics play the same role with many-body Newtonian equations in physics. Accordingly, each solution of the general equilibrium equations can be regarded as a possible microstate of the economic system.…
A recent line of work provides new statistical tools based on game-theory and achieves safe anytime-valid inference without assuming regularity conditions. In particular, the framework of universal inference proposed by Wasserman, Ramdas…
We introduce a broad class of analytically solvable processes on networks. In the special case, they reduce to random walk and consensus process - two most basic processes on networks. Our class differs from previous models of interactions…
Path-dependent stochastic processes are often non-ergodic and observables can no longer be computed within the ensemble picture. The resulting mathematical difficulties pose severe limits to the analytical understanding of path-dependent…
The ratio of two consecutive level spacings has emerged as a very useful metric in investigating universal features exhibited by complex spectra. It does not require the knowledge of density of states and is therefore quite convenient to…
Doubly intractable distributions arise in many settings, for example in Markov models for point processes and exponential random graph models for networks. Bayesian inference for these models is challenging because they involve intractable…
It is argued that a Gibbsian formula for the space-time distribution of microscopic trajectories of a nonequilibrium system provides a unifying framework for recent results on the fluctuations of the entropy production. The variable entropy…
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…
A considerable number of systems have recently been reported in which Brownian yet non-Gaussian dynamics was observed. These are processes characterised by a linear growth in time of the mean squared displacement, yet the probability…
While run-and-tumble particles are a foundational model for self-propelled particles as bacteria or Janus particles, the analytical derivation of their steady state from the microscopic details is still an open problem. By directly modeling…
We study the stationary fluctuations of independent run-and-tumble particles. We prove that the joint densities of particles with given internal state converges to an infinite dimensional Ornstein-Uhlenbeck process. We also consider an…
. We study the evolution of the distribution of eigenvalues of a $N\times N$ matrix subject to a random perturbation drawn from (i) a generalized Gaussian ensemble (ii) a non-Gaussian ensemble with a measure variable under the change of…
This paper proposes a simple mathematical model of non-stationary and non-linear stochastic dynamics, which approximates a (globally) non-stationary and non-linear stochastic process by its locally (or \emph{"piecewise"}) stationary…
Consider the infinite Atlas model: a semi-infinite collection of particles driven by independent standard Brownian motions with zero drifts, except for the bottom-ranked particle which receives unit drift. We derive a continuum…
Gaussian processes (GPs) are commonplace in spatial statistics. Although many non-stationary models have been developed, there is arguably a lack of flexibility compared to equipping each location with its own parameters. However, the…
We propose a method to derive the stationary size distributions of a system, and the degree distributions of networks, using maximisation of the Gibbs-Shannon entropy. We apply this to a preferential attachment-type algorithm for systems of…
Nowadays many tools, e.g. fluctuation relations, are available to characterize the statistical properties of non-equilibrium systems. However, most of these tools rely on the assumption that the driving noise is normally distributed. Here…