Related papers: Scaling limit for a drainage network model
The Brownian web is a collection of one-dimensional coalescing Brownian motions starting from every point in space and time, while the Brownian net is an extension that also allows branching. We show here that the Brownian net is the…
The Brownian web is a collection of one-dimensional coalescing Brownian motions starting from everywhere in space and time, and the Brownian net is a generalization that also allows branching. They appear in the diffusive scaling limits of…
We introduce a new metric for collections of aged paths and a robust set of criteria for compactness for a set of collection of aged paths in the topology corresponding to this metric. We show that the distribution of stable webs ($1<…
We investigated the scaling and topology of engineered urban drainage networks (UDNs) in two cities, and further examined UDN evolution over decades. UDN scaling was analyzed using two power-law characteristics widely employed for river…
The Brownian net, which has recently been introduced by Sun and Swart [SS08], and independently by Newman, Ravishankar and Schertzer [NRS08], generalizes the Brownian web by allowing branching. In this paper, we study the structure of the…
A pore-scale model is introduced for two-phase flow in dense packings of polydisperse spheres. The model is developed as a component of a more general hydromechanical coupling framework based on the discrete element method, which will be…
Recently, a novel family of biologically plausible online algorithms for reducing the dimensionality of streaming data has been derived from the similarity matching principle. In these algorithms, the number of output dimensions can be…
We extend the results on the RG flow in the next to leading order to the case of the supersymmetric minimal models SM_p for p>> 1. We explain how to compute the NS and Ramond fields conformal blocks in the leading order in 1/p and follow…
We explore the concepts of self-similarity, dimensionality, and (multi)scaling in a new family of recursive scale-free nets that yield themselves to exact analysis through renormalization techniques. All nets in this family are self-similar…
We present an alternative finite-size approach to a set of parity conserving interfaces involving attachment, dissociation, and detachment of extended objects in 1+1 dimensions. With the aid of a nonlocal construct introduced by Barma and…
In this paper, we show a large deviation principle for certain sequences of static Schr\"{o}dinger bridges, typically motivated by a scale-parameter decreasing towards zero, extending existing large deviation results to cover a wider range…
We study the structure of a uniformly randomly chosen partial order of width 2 on n elements. We show that under the appropriate scaling, the number of incomparable elements converges to the height of a one dimensional Brownian excursion at…
Dual descent methods are commonly used to solve network flow optimization problems, since their implementation can be distributed over the network. These algorithms, however, often exhibit slow convergence rates. Approximate Newton methods…
In a recent work, we proved that under diffusive scaling, the collection of rightmost infinite open paths in a supercritical oriented percolation configuration on the space-time lattice Z^2 converges in distribution to the Brownian web. In…
We introduce a new phenomenological one-scale model for the evolution of domain wall networks, and test it against high-resolution field theory numerical simulations. We argue that previous numerical estimates of wall velocities are…
We consider a stochastic model of Internet congestion control, introduced by Massouli\'{e} and Roberts [Telecommunication Systems 15 (2000) 185--201], that represents the randomly varying number of flows in a network where bandwidth is…
Previously, Sarkar and Sun have shown that for supercritical oriented percolation in dimension $1+1$, the set of rightmost infinite open paths converges to the Brownian web after proper centering and scaling. In this note, we show that a…
For three constrained Brownian motions, the excursion, the meander, and the reflected bridge, the densities of the maximum and of the time to reach it were expressed as double series by Majumdar, Randon-Furling, Kearney, and Yor (2008).…
In S. Giombi, I. Klebanov, F. Popov, S. Prakash and G. Tarnopolsky, {\it Phys. Rev.} {\bf D} 98 (2018) 10, 105005, a prismatic tensor model was introduced. We study here the diagrammatics and the double scaling limit of this model, using…
This article provides a scaling limit for a family of skew interacting Brownian motions in the context of mesoscopic interface models. Let $d\in\mathbb N$, $y_1,\dots,y_M\in\mathbb R$ and $f\in C_b(\mathbb R)$ be fixed. For each…