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As machine-learning models become larger and more complex, they require faster and more energy-efficient hardware to perform computations. Conventional digital computers are struggling to keep up.
SCALING LIMITS OF RECURRENT EXCITED RANDOM WALKS ON INTEGERS
Limit random walk RECURRENT EXCITED
2015/9/29
We describe scaling limits of recurrent excited random walks (ERWs) on
Z in i.i.d. cookie environments with a bounded number of cookies per site. We allow
both positive and negative excitations.
Scaling Limits for Internal Aggregation Models with Multiple Sources
Scaling Limits Internal Aggregation Models Multiple Sources
2015/8/14
We study the scaling limits of three different aggregation models on Zd: internal DLA, in which particles perform random walks until reaching an unoccupied site; the rotor-router model, in which parti...
Schroder's problems and scaling limits of random trees
Schroder's problems Probability scaling limits of random trees
2011/8/31
Abstract: In a classic paper Schr\"oder posed four combinatorial problems about the number of certain types of bracketings of words and sets. Here we address what these bracketings look like on averag...
The Topology of Scaling Limits of Positive Genus Random Quadrangulations
Topology of Scaling Limits Positive Genus Random Quadrangulations
2011/2/22
We discuss scaling limits of large bipartite quadrangulations of positive genus. For a given g,
we consider, for every n 1, a random quadrangulation qn uniformly distributed over the set
of all ro...
We revisit the study of the maximally singular point in the Coulomb branch of 4d N=2 SU(N) gauge theory with N_f=2n flavors for N_f<2N. When n >= 2, we find that the low-energy physics is described b...
Scaling Limits for Multispecies Statistical Mechanics Mean-Field Models
Multispecies Statistical Mechanics Mean-Field Models
2010/11/19
We study the limiting thermodynamic behavior of the normalized sums of spins in multi-species Curie-Weiss models. We find sufficient conditions for the limiting random vector to be Gaussian (or to ha...
Double scaling limits of random matrices and minimal (2m,1) models: the merging of two cuts in a degenerate case
Double scaling limits minimal (2m,1) models random matrices
2010/4/2
In this article, we show that the double scaling limit correlation functions of a random matrix model when two cuts merge with degeneracy $2m$ (i.e. when $y\sim x^{2m}$ for arbitrary values of the int...
On the sphericity of scaling limits of random planar quadrangulations
scaling limits random planar quadrangulations
2009/3/19
We give a new proof of a theorem by Le Gall and Paulin, showing that scaling limits of random planar quadrangulations are homeomorphic to the 2-sphere. The main geometric tool is a reinforcement of th...