Related papers: Meander, Folding and Arch Statistics
We study the statistics of height and balanced height in the binary search tree problem in computer science. The search tree problem is first mapped to a fragmentation problem which is then further mapped to a modified directed polymer…
The fluctuations of two-dimensional extended objects membranes is a rich and exciting field with many solid results and a wide range of open issues. We review the distinct universality classes of membranes, determined by the local order,…
We discuss various aspects of the randomly interacting directed polymers with emphasis on the phases and phase transition. We also discuss the behaviour of overlaps of directed paths in a random medium.
Spaces of quasi-invariant measures supplied with different topologies are studied. Their embeddings, projective decompositions, conditions for their metrizability are investigated. Theorems about convergence of nets of quasi-invariant…
We study two types of random matrix ensembles that emerge when considering the same probability measure on partitions. One is the Meixner ensemble with a hard wall and the other are two families of unitary matrix models, with weight…
We introduce simple conditions ensuring that invariant distributions of a Feller Markov chain on a compact Riemannian manifold are absolutely continuous with a lower semi-continuous, continuous or smooth density with respect to the…
The notion of a mesh pattern was introduced recently, but it has already proved to be a useful tool for description purposes related to sets of permutations. In this paper we study eight mesh patterns of small lengths. In particular, we…
Statistical analysis of a graph often starts with embedding, the process of representing its nodes as points in space. How to choose the embedding dimension is a nuanced decision in practice, but in theory a notion of true dimension is…
In these lecture notes we present some connections between random matrices, the asymmetric exclusion process, random tilings. These three apparently unrelated objects have (sometimes) a similar mathematical structure, an interlacing…
In this work a new strategy is proposed in order to build analytic and microscopic models of fluctuating polymer rings subjected to topological constraints. The topological invariants used to fix these constraints belong to a wide class of…
This is a brief survey of certain constants associated with random lattice models, including self-avoiding walks, polyominoes, the Lenz-Ising model, monomers and dimers, ice models, hard squares and hexagons, and percolation models.
The problem of counting polymer coverings on the rectangular lattices is investigated. In this model, a linear rigid polymer covers $k$ adjacent lattice sites such that no two polymers occupy a common site. Those unoccupied lattice sites…
This article provides an overview on the statistical modeling of complex data as increasingly encountered in modern data analysis. It is argued that such data can often be described as elements of a metric space that satisfies certain…
In this paper we investigate the conformation statistics of a Gaussian chain embedded in a medium of finite size, in the presence of quenched random obstacles. The similarities and differences between the case of random obstacles and the…
Analytical relations for the mechanical response of single polymer chains are valuable for modeling purposes, on both the molecular and the continuum scale. These relations can be obtained using statistical thermodynamics and an idealized…
Harmonic maps are nonlinear extensions of harmonic functions. They are critical points of natural energy functionals between Riemannian manifolds. Such type of problems appear in Physics, Geometry of Finance and the study of regularity and…
Quantized, compact graphs were shown to be excellent paradigms for quantum chaos in bounded systems. Connecting them with leads to infinity we show that they display all the features which characterize scattering systems with an underlying…
In polymer physics it is typically assumed that excluded volume interactions are effectively screened in polymer melts. Hence, chains could be described by an effective random walk without excluded volume interactions. In this letter, we…
The two-dimensional cage model for polymer motion is discussed with an emphasis on the effect of sideways motions, which cross the barriers imposed by the lattice. Using the Density Matrix Method as a solver of the Master Equation, the…
Using non-equilibrium Brownian dynamics computer simulations, we have investigated the steady state statistics of a polymer chain under three different shear environments: i) linear shear flow in the bulk (no walls), ii) shear vorticity…