Related papers: On the statistical physics of directed polymers in…
In this paper we investigate the asymptotic optimality property of a randomized sampling based motion planner, namely RRT. We prove that a RRT planner is not an asymptotically optimal motion planner. Our result, while being consistent with…
We construct a phenomenological theory of self-localization of directed polymers in d+1 dimensions. In d=1 we show that the polymer is always self-localized, whereas in d=2 there is a phase transition between localized and free states. We…
The statistical mechanics of directed line-like objects, such as directed polymers in an external field, strands of dipoles in both ferro- and electrorheological fluids, and flux lines in high-$T_{\tiny C}$ superconductors bears a close…
We study models for a directed polymer in a random environment (DPRE) in which the polymer traverses a hierarchical diamond graph and the random environment is defined through random variables attached to the vertices. For these models, we…
We introduce a new spanning tree model called the random spanning tree in random environment (RSTRE), which interpolates between the uniform spanning tree and the minimum spanning tree as the inverse temperature (disorder strength) $\beta$…
For a directed polymer in a random medium lying on an infinite cylinder, that is in 1+1 dimensions with finite width and periodic boundary conditions on the transverse direction, the winding number is simply the algebraic number of turns…
The directed polymer in a 1+3 dimensional random medium is known to present a disorder-induced phase transition. For a polymer of length $L$, the high temperature phase is characterized by a diffusive behavior for the end-point displacement…
In this thesis, we study a new disordered system called random spanning tree in random environment (RSTRE) across different families of graphs with varying disorder distributions. We examine several observables as functions of the disorder…
The conformational statistics of ring polymers in melts or dense solutions is strongly affected by their quenched microscopic topological state. The effect is particularly strong for non-concatenated unknotted rings, which are known to…
We uncover a nontrivial signature of the hierarchical structure of quasi-degenerate random directed polymers (RDPs) at zero temperature in 1+1 dimensional lattices. Using a cylindrical geometry with circumference $8 \leq W \leq 512$, we…
This paper investigates the computational geometry relevant to calculations of the Frechet mean and variance for probability distributions on the phylogenetic tree space of Billera, Holmes and Vogtmann, using the theory of probability…
We consider the fluctuations of the free energy of positive temperature directed polymers in thin rectangles (N,N^{\alpha}), \alpha < 3/14. For general weight distributions with finite fourth moment we prove that the distribution of these…
Because of a close blood relationship between directed percolation & directed polymers in random media, the latter's journey to asymptotic scaling can be greatly retarded by an uninformed choice of departure point; i.e., the bare-bond PDF…
In this article, we present an invariance principle for the paths of the directed random polymer in space dimension two in the subcritical intermediate disorder regime. More precisely, the distribution of diffusively rescaled polymer paths…
The statistical mechanics of a treelike polymer in a confining volume is relevant to the packaging of the genome in RNA viruses. Making use of the mapping of the grand partition function of this system onto the statistical mechanics of a…
We show that for many models of random trees, the independence number divided by the size converges almost surely to a constant as the size grows to infinity; the trees that we consider include random recursive trees, binary and $m$-ary…
Given a finite planar graph, a grove is a spanning forest in which every component tree contains one or more of a specified set of vertices (called nodes) on the outer face. For the uniform measure on groves, we compute the probabilities of…
Random forests remain among the most popular off-the-shelf supervised machine learning tools with a well-established track record of predictive accuracy in both regression and classification settings. Despite their empirical success as well…
We construct and study a family random continuum polymer measures $\mathbf{M}_{r}$ corresponding to limiting partition function laws recently derived in a weak-coupling regime of polymer models on hierarchical graphs with marginally…
This work studies the statistical implications of using features comprised of general linear combinations of covariates to partition the data in randomized decision tree and forest regression algorithms. Using random tessellation theory in…