相关论文: Scaling limit for a drainage network model

Many real life networks present an average path length logarithmic with the number of nodes and a degree distribution which follows a power law. Often these networks have also a modular and self-similar structure and, in some cases -…

Several new network information dimension definitions have been proposed in recent decades, expanding the scope of applicability of this seminal tool. This paper proposes a new definition based on Deng entropy and d-summability (a concept…

Despite prevailing concerns that the current Internet interdomain routing system will not scale to meet the needs of the 21st century global Internet, networking research has not yet led to the construction of a new routing architecture…

We imitate the spectrum character of one-dimensional disorder system with our new rain model. It has been shown that the transmission spectrum can be approximately characterized by the model, which include some coupled lorentzian…

Coalescing simple random walks in the plane form an infinite tree. A natural directed distance on this tree is given by the number of jumps between branches when one is only allowed to move in one direction. The Brownian web distance is the…

We give computable bounds on the rate of convergence of the transition probabilities to the stationary distribution for a certain class of geometrically ergodic Markov chains. Our results are different from earlier estimates of Meyn and…

We introduce a natural measure on bi-infinite random walk trajectories evolving in a time-dependent environment driven by the Langevin dynamics associated to a gradient Gibbs measure with convex potential. We derive an identity relating the…

Using the flow governing equation approach to similarity, Weyburne (D. Weyburne, arXiv:1701.02364, 2016) recently showed that for 2-D turbulent boundary layer flows, the Prandtl Plus scalings are NOT, in general, the proper similarity…

Using a simple model with link removals as well as link additions, we show that an evolving network is scale free with a degree exponent in the range of (2, 4]. We then establish a relation between the network evolution and a set of…

Let $(\mathcal{M},g)$ be a closed Riemannian manifold. The $\textit{ second order approximation}$ to the perturbative renormalization group flow for the nonlinear sigma model (RG-2 flow) is given by : \[ \frac{\partial }{\partial t} \, g(t)…

We prove that properly rescaled large planar Eulerian triangulations converge to the Brownian map. This result requires more than a standard application of the methods that have been used to obtain the convergence of other families of…

We analyze the convergence rate of gradient flows on objective functions induced by Dropout and Dropconnect, when applying them to shallow linear Neural Networks (NNs) - which can also be viewed as doing matrix factorization using a…

In this paper, we study in the Markovian case the rate of convergence in the Wasserstein distance of an approximation of the solution to a BSDE given by a BSDE which is driven by a scaled random walk as introduced in Briand, Delyon and…

We analyze the structure of networks minimizing the global resistance to flow (or dissipated energy) with respect to two different constraints: fixed total channel volume and fixed total channel surface area. First, we determine the shape…

In this paper, we established a large deviation principle for stochastic models of incompressible second grade fluids. The weak convergence method introduced by \cite{Budhiraja-Dupuis} plays an important role.

Consider the d-dimensional lattice Z^d where each vertex is ``open'' or ``closed'' with probability p or 1-p, respectively. An open vertex v is connected by an edge to the closest open vertex w such that the dth co-ordinates of v and w…

The renormalisation group (RG) flow on the space of couplings of a simple model with two couplings is examined. The model considered is that of a single component scalar field with $\phi^4$ self interaction coupled, via Yukawa coupling, to…

Random planar maps are considered in the physics literature as the discrete counterpart of random surfaces. It is conjectured that properly rescaled random planar maps, when conditioned to have a large number of faces, should converge to a…

Let x and y be chosen uniformly in a graph G. We find the limiting distribution of the length of a loop-erased random walk from x to y on a large class of graphs that include the discrete torus in dimensions 5 and above. Moreover, on this…

In recent work by L. Levine and Y. Peres, it was observed that three models for particle aggregation on the lattice - the divisible sandpile, rotor-router aggregation, and internal diffusion limited aggregation - share a common scaling…