相关论文: The conditional Gaussian multiplicative chaos stru…
We study measures on $\mathbb{R}^d$ which are induced by a class of infinite and recursive iterations in symbolic dynamics. Beginning with a finite set of data, we analyze prescribed recursive iteration systems, each involving subdivisions.…
We present a unified scaling theory for the structural behavior of polymers embedded in a disordered energy substrate. An optimal polymer configuration is defined as the polymer configuration that minimizes the sum of interacting energies…
We investigate the evolution of the density-density correlations in the isoscalar critical condensate formed at the QCD critical point. The initial equilibrium state of the system is characterized by a fractal measure determining the…
We investigate in some detail a "variational mass" expansion approach, generalized from a similar construction developed in the Gross-Neveu model, to evaluate the basic order parameters of the dynamical breaking of the $SU(2)_L \times…
We study the total mass of high points in a random model for the Riemann-Zeta function. We consider the same model as in [8], [2], and build on the convergence to 'Gaussian' multiplicative chaos proved in [14]. We show that the total mass…
A R\"ossler model perturbed with a piecewise constant function is investigated. The perturbation function used in the model is constructed by means of the logistic map. In the absence of the perturbation the system is assumed to possess two…
We determine the exact threshold of the extended Seiberg bound for the existence of correlation functions in the boundary Liouville conformal field theory in the unit disk. In probabilistic terms, our result is a toolbox yielding the…
Constant dimension codes (CDCs), as special subspace codes, have received a lot of attention due to their application in random network coding. This paper introduces a family of new codes, called rank metric codes with given ranks (GRMCs),…
Constraints on cosmological parameters from large-scale structure have traditionally been obtained from two-point statistics. However, non-linear structure formation renders these statistics insufficient in capturing the full information…
While extensive research has been conducted on chaos emerging from a dynamical system's temporal dynamics, our research examines extreme sensitivity to initial conditions in discrete-time dynamical systems from a geometrical perspective.…
Recent observations of globular clusters (GCs) suggest that elemental abundance variations may exist between first-generation (1G) stars. We propose that metal abundance ('metallicity') spreads within GC forming giant molecular clouds…
We show that, for general convolution approximations to a large class of log-correlated fields, including the 2d Gaussian free field, the critical chaos measures with derivative normalisation converge to a limiting measure {\mu}'. This…
The standard logistic map, $x'=ax(1-x)$, serves as a paradigmatic model to demonstrate how apparently simple non-linear equations lead to complex and chaotic dynamics. In this work we introduce and investigate its matrix analogue defined…
We continue the study of the Fourier coefficients of Gaussian multiplicative chaos (GMC) recently initiated by Garban and Vargas. We show that if $\{c_n\}_{n\geq 1}$ are the Fourier coefficients of critical GMC on the unit interval, then…
Gaussian processes (GPs) are frequently used in machine learning and statistics to construct powerful models. However, when employing GPs in practice, important considerations must be made, regarding the high computational burden,…
We present new, short and self-contained proofs of the convergence (with an adequate renormalization) of four different sequences to the critical Gaussian Multiplicative Chaos:(a) the derivative martingale (b) the critical martingale (c)…
We consider the disordered monomer-dimer model on cylinder graphs $\mathcal{G}_n$, i.e., graphs given by the Cartesian product of the line graph on $n$ vertices, and a deterministic graph. The edges carry i.i.d. random weights, and the…
The mean area of a two-dimensional Gaussian ring of $N$ monomers is known to diverge when the ring is subject to a critical pressure differential, $p_c \sim N^{-1}$. In a recent publication [Eur. Phys. J. E 19, 461 (2006)] we have shown…
We propose a novel combinatorial algorithm for efficient generation of Hamiltonian walks and cycles on a cubic lattice, modeling the conformations of lattice toy proteins. Through extensive tests on small lattices (allowing complete…
Although granular materials are the second most processed in industry after water, the theoretical study of granules-structure interactions is not as advanced as that of fluid-structure interactions due to the lack of a unified view of the…