Related papers: Functional Limit Theorems for Dynamical Systems wi…
Cluster indices describe extremal behaviour of stationary time series. We consider their sliding blocks estimators. Using a modern theory of multivariate, regularly varying time series, we obtain central limit theorems under conditions that…
A univariate clustering criterion for stationary processes satisfying a $\beta$-mixing condition is proposed extending the work of \cite{KB2} to the dependent setup. The approach is characterized by an alternative sample criterion function…
An order parameter, termed the maximal row correlation, is proposed for classical spin systems. Monte Carlo simulations on various Potts models suggest that this order parameter is applicable to a broad range of spin systems, including…
Kinetic and hydrodynamic theories are widely employed for describing the collective behaviour of active matter systems. At the fluctuating level, these have been obtained from explicit coarse-graining procedures in the limit where each…
In this article, we investigate the convergence behavior of two classes of gathering protocols with fixed circulant topologies using tools from dynamical systems. Given a fixed number of mobile entities moving in the Euclidean plane, we…
This survey paper discusses behaviour of higher-order correlations for one-parameter dynamical systems and more generally for dynamical systems arising from group actions. In particular, we present a self-contained proof of quantitative…
We review several competing chaining methods to estimate the supremum, the diameter of the range or the modulus of continuity of a stochastic process in terms of tail bounds of their two-dimensional distributions. Then we show how they can…
Various functional limit theorems for partial sum processes of strictly stationary sequences of regularly varying random variables in the space of cadlag functions $D[0,1]$ with one of the Skorohod topologies have already been obtained. The…
Recently, for the joint partial sum and partial maxima processes constructed from linear processes with independent identically distributed innovations that are regularly varying with tail index $\alpha \in (0, 2)$, a functional limit…
In this work we derive limit theorems for trawl processes. First,we study the asymptotic behaviour of the partial sums of the discretized trawl process $(X_{i\Delta_{n}})_{i=0}^{\lfloor nt\rfloor-1}$, under the assumption that as…
We consider a Markov chain of point processes such that each state is a super position of an independent cluster process with the previous state as its centre process together with some independent noise process. The model extends earlier…
This thesis develops exact analytical tools to study strongly correlated stochastic systems, with a focus on extreme value statistics, gap statistics, and full counting statistics in multi-particle processes. A central contribution is the…
We study the asymptotic nature of geometric structures formed from a point cloud of observations of (generally heavy tailed) distributions in a Euclidean space of dimension greater than one. A typical example is given by the Betti numbers…
Correlation functions of CFT operators with infinite scaling dimension are rich, multifaceted objects that describe physics ranging across classical holography, black hole dynamics, and flat-space scattering amplitudes. In this work, we…
We study the spontaneous motion, binary collisions, and collective dynamics of "polar disks", i.e. purpose-built particles which, when vibrated between two horizontal plates, move coherently along a direction strongly correlated to their…
Some models of clustering processes are formulated and analytically solved employing generating functions methods. Those models include events which result from combined action of the coagulation and fragmentation processes. Fragmentation…
We consider the dynamics of systems of self propelling particles with nonholonomic constraints. A continuum model for a discrete algorithm used in works by T. Vicsek et al. is proposed. For a case of planar geometry the finite flocking…
We formulate a novel technique for the detection of functional clusters in discrete event data. The advantage of this algorithm is that no prior knowledge of the number of functional groups is needed, as our procedure progressively combines…
There are rich emergent phase behaviors in non-equilibrium active systems. Flocking and clustering are two representative dynamic phases. The relationship between these two phases is still unclear. In the paper, we numerically investigate…
We introduce the cluster index of a multivariate regularly varying stationary sequence and characterize the index in terms of the spectral tail process. This index plays a major role in limit theory for partial sums of regularly varying…