Related papers: Branched Polymers Re-Revisited
We study directed polymers subject to a quenched random potential in d transversal dimensions. This system is closely related to the Kardar-Parisi-Zhang equation of nonlinear stochastic growth. By a careful analysis of the perturbation…
While Flory theories provide an extremely useful framework for understanding the behavior of interacting, randomly branching polymers, the approach is inherently limited. Here we use a combination of scaling arguments and computer…
Let H be a non-semisimple Hopf algebra of dimension 2p^2 over an algebraically closed field of characteristic zero, where p is an odd prime. We prove that H or H^* is pointed, which completes the classification for Hopf algebras of these…
In the first part of the paper we prove a bi-parameter version of a well known multilinear theorem of Coifman and Meyer. As a consequence, we generalize the Kato-Ponce inequality in nonlinear PDE, obtaining a fractional Leibnitz rule for…
We show that the multiplicity of a plane analytic 1-form is a bound for the number of Puiseux exponents of a (formal or convergent) branch. This is true whether the associated foliation is dicritical or not.
It is well known that in 1D the cross section of a point scatterer increases along with the scatterer's strength (potential). In this paper we show that this is an exceptional case, and in all the other cases, where a point defect has a…
This paper provides a convenient and practical method to compute the homology and intersection pairing of a branched double cover of the 4-ball. To projections of links in the 3-ball, and to projections of surfaces in the 4-ball into the…
The phenomena that cause a value of a polynomial function to be a bifurcation one are yet to be described when the fibers have dimension higher than $1$. In this note, the main result is the construction of a polynomial submersion function…
We characterize when bivariate real analytic functions are "dimension expanding" when applied to a Cartesian product. If $P$ is a bivariate real analytic function that is not locally of the form $P(x,y) = h(a(x) + b(y))$, then whenever $A$…
The main objects of the investigation presented in this paper are branched-continued-fraction representations of ratios of contiguous hypergeometric series and type II multiple orthogonal polynomials on the step-line with respect to linear…
We contend that the arguments provided in Phys. Rev. Lett. 130, 016001 (2023), purporting to show the absence of off-diagonal long-range order in hcp $^4$He dislocation cores are misleading and incorrect. In particular, the one-body density…
We solve a class of branched polymer models coupled to spin systems and show that they have no phase transition and are either always magnetized or never magnetized depending on the branching weights. By comparing these results with…
In this paper we study the structure of polynomials of degree three and four that have high bias or high Gowers norm, over arbitrary prime fields. In particular we obtain the following results. 1. We give a canonical representation for…
This paper has been withdrawn by the author due to a mistake in the section 4.
A seminal theorem of Tverberg states that any set of $T(r,d)=(r-1)(d+1)+1$ points in $\mathbb{R}^d$ can be partitioned into $r$ subsets whose convex hulls have non-empty $r$-fold intersection. Almost any collection of fewer points in…
The determinant method in the conformal bootstrap is applied for the critical phenomena of a single polymer in arbitrary $D$ dimensions. The scale dimensions (critical exponents) of the polymer ($2< D \le 4$) and the branched polymer ($3 <…
We investigate the statistical properties of a randomly branched 3--functional $N$--link polymer chain without excluded volume, whose one point is fixed at the distance $d$ from the impenetrable surface in a 3--dimensional space. Exactly…
We make a new attempt at the recently suggested program to express knot polynomials through topological vertices, which can be considered as a possible approach to the tangle calculus: we discuss the Macdonald deformation of the relation…
This dissertation investigates the geometric combinatorics of convex polytopes and connections to the behavior of the simplex method for linear programming. We focus our attention on transportation polytopes, which are sets of all tables of…
We look for partition theorems for large subtrees for suitable uncountable trees and colourings. We concentrate on sub-trees of $^{\kappa \ge} 2$ expanded by a well ordering of each level. Unlike earlier works, we do not ask the embedding…