Related papers: Assouad spectrum thresholds for some random constr…
We consider nearest neighbour spatial random permutations on $\mathbb{Z}^d$. In this case, the energy of the system is proportional the sum of all cycle lengths, and the system can be interpreted as an ensemble of edge-weighted, mutually…
We study asymptotic properties of supercritical Galton-Watson (GW) branching processes in the asymptotic where the mean of the offspring distribution approaches 1 from above. We show that the population-size distribution of the GW branching…
We investigate the random continuous trees called L\'evy trees, which are obtained as scaling limits of discrete Galton-Watson trees. We give a mathematically precise definition of these random trees as random variables taking values in the…
The uniform disconnectedness is an important invariant property under bi-Lipschitz mapping, and the Assouad dimension $\dim _{A}X<1$ implies the uniform disconnectedness of $X$. According to quasi-Lipschitz mapping, we introduce the…
We derive an upper bound for the Assouad dimension of visible parts of self-similar sets generated by iterated function systems with finite rotation groups and satisfying the open set condition. The bound is valid for all visible parts and…
The spectral properties of interacting strongly chaotic systems are investigated for growing interaction strength. A very sensitive transition from Poisson statistics to that of random matrix theory is found. We introduce a new random…
We consider infinite Galton-Watson trees without leaves together with i.i.d.~random variables called marks on each of their vertices. We define a class of flow rules on marked Galton-Watson trees for which we are able, under some algebraic…
The field theoretic renormalization group and operator product expansion are applied to the problem of a passive scalar advected by the Gaussian nonsolenoidal velocity field with finite correlation time, in the presence of large-scale…
We consider the random deposition of objects of variable width and height over a line. The successive additions of these structures create a random interface. We focus on the regime of heavy tailed distributions of the structure width. When…
We introduce a new oriented evolving graph model inspired by biological networks. A node is added at each time step and is connected to the rest of the graph by random oriented edges emerging from older nodes. This leads to a statistical…
We derive theorems which outline explicit mechanisms by which anomalous scaling for the probability density function of the sum of many correlated random variables asymptotically prevails. The results characterize general anomalous scaling…
We show that self-conformal subsets of $\mathbb{R}$ that do not satisfy the weak separation condition have full Assouad dimension. Combining this with a recent results by K\"aenm\"aki and Rossi we conclude that an interesting dichotomy…
We determine the Gromov--Hausdorff--Prokhorov scaling limits and local limits of Kemp's $d$-dimensional binary trees and other models of supertrees. The limits exhibit a root vertex with infinite degree and are constructed by rescaling…
We study the breaking of supersymmetry in five-dimensional (5d) warped spaces, using the Randall-Sundrum model as a prototype. In particular, we present a supersymmetry-breaking mechanism which has a geometrical origin, and consists of…
In this article, we study a simple random walk on a decorated Galton-Watson tree, obtained from a Galton-Watson tree by replacing each vertex of degree $n$ with an independent copy of a graph $G_n$ and gluing the inserted graphs along the…
We derive the scaling dimension of antisymmetric tensor operators in the boundary theory of the AdS/CFT correspondence using a functional integral representation of the boundary-to-boundary propagators of their dual fields in the bulk. We…
Fractal/non-fractal morphological transitions allow for the systematic study of the physics behind fractal morphogenesis in nature. In these systems, the fractal dimension is considered a non-thermal order parameter, commonly and…
A numerical study of the transfer across random fractal surfaces shows that their responses are very close to the response of deterministic model geometries with the same fractal dimension. The simulations of several interfaces with…
For random matrices with block correlation structure we show that the fluctuations of linear eigenvalue statistics are Gaussian on all mesoscopic scales with universal variance which coincides with that of the Gaussian unitary or Gaussian…
We discuss a random matrix model of systems with an approximate symmetry and present the spectral fluctuation statistics and eigenvector characteristics for the model. An acoustic resonator like, e.g., an aluminium plate may have an…