Related papers: Generalized stealthy hyperuniform processes : maxi…
It has been shown numerically that systems of particles interacting with "stealthy" bounded, long-ranged pair potentials (similar to Friedel oscillations) have classical ground states that are, counterintuitively, disordered, hyperuniform…
The {\it number rigidity} of a stationary point process $\mathsf{P}$ entails that for a bounded set $A$ the knowledge of $\mathsf{P}$ on $A^{c}$ a.s. determines $\mathsf{P}(A)$; the $k$-order rigidity means the moments of $\mathsf{P}1_{A}$…
We study exclusion processes on the integer lattice in which particles change their velocities due to stickiness. Specifically, whenever two or more particles occupy adjacent sites, they stick together for an extended period of time, and…
The diffraction of stochastic point sets, both Bernoulli and Markov, and of random tilings with crystallographic symmetries is investigated in rigorous terms. In particular, we derive the diffraction spectrum of 1D random tilings, of…
We prove that each discrete set in the Euclidean space that has bounded changes under every translation is a bounded perturbation of a square lattice, i.e., a uniformly spread set in the sense of Laszkovich. In particular, the support of…
Recently we extended the concept of intrinsic ultracontractivity to non-symmetric semigroups and proved that for a large class of non-symmetric diffusions Z with measure-valued drift and potential, the semigroup of Z^D (the process obtained…
A universal law for the supercritical bifurcation shape of transverse one-dimensional (1D) systems in presence of additive noise is given. The stochastic Langevin equation of such systems is solved by using a Fokker-Planck equation leading…
Time-irreversible stochastic processes are frequently used in natural sciences to explain non-equilibrium phenomena and to design efficient stochastic algorithms. Our main goal in this thesis is to analyse their dynamics by means of large…
In this paper, we study the Ornstein-Uhlenbeck bridge process (i.e. the Ornstein-Uhlenbeck process conditioned to start and end at fixed points) constraints to have a fixed area under its path. We present both anticipative (in this case, we…
We derive functional convergence of the partial maxima stochastic processes of multivariate linear processes with weakly dependent heavy-tailed innovations and random coefficients. The convergence takes place in the space of…
We consider vector valued, unit variance Gaussian processes defined over stratified manifolds and the geometry of their excursion sets. In particular, we develop an explicit formula for the expectation of all the Lipschitz--Killing…
Wu and Verd\'u developed a theory of almost lossless analog compression, where one imposes various regularity conditions on the compressor and the decompressor with the input signal being modelled by a (typically infinite-entropy)…
We consider a one-dimensional stationary time series of fixed duration $T$. We investigate the time $t_{\rm m}$ at which the process reaches the global maximum within the time interval $[0,T]$. By using a path-decomposition technique, we…
Hyperuniform many-body systems in $d$-dimensional Euclidean space are characterized by completely suppressed (normalized) infinite-wavelength density fluctuations, and appear to be endowed with novel exotic physical properties. In this…
For a Dawson-Watanabe superprocess $X$ on $\mathbb{R}^d$, it is shown in Perkins (1990) that if the underlying spatial motion belongs to a certain class of L\'evy processes that admit jumps, then with probability one the closed support of…
For a Dawson-Watanabe superprocess $X$ on $\mathbb{R}^d$, it is shown in Perkins (1990) that if the underlying spatial motion belongs to a certain class of L\'evy processes that admit jumps, then with probability one the closed support of…
We develop a fluctuation theory of connectivities for subcritical random cluster models. The theory is based on a comprehensive nonperturbative probabilistic description of long connected clusters in terms of essentially one-dimensional…
In this paper, we prove a universality result for the limiting distribution of persistence diagrams arising from geometric filtrations over random point processes. Specifically, we consider the distribution of the ratio of persistence…
In this article, we investigate the condensation phenomena for a class of nonreversible zero-range processes on a fixed finite set. By establishing a novel inequality bounding the capacity between two sets, and by developing a robust…
In this article, we investigate posterior convergence in nonparametric regression models where the unknown regression function is modeled by some appropriate stochastic process. In this regard, we consider two setups. The first setup is…