arXiv subjects

Rui Dong

Publications and source records attributed to Rui Dong.

40 records · Page 3Linked to original sources

arXiv2012

Structured epitaxial graphene: growth and properties

Graphene is generally considered to be a strong candidate to succeed silicon as an electronic material. However, to date, it actually has not yet demonstrated capabilities that exceed standard semiconducting materials. Currently demonstrated viable graphene devices are essentially limited to micron size ultrahigh frequency analog field effect transistors and quantum Hall effect devices for metrology. Nanoscopically patterned graphene tends to have disordered edges that severely reduce mobilities thereby obviating its advantage over other materials. Here we show that graphene grown on structured silicon carbide surfaces overcomes the edge roughness and promises to provide an inroad into nanoscale patterning of graphene. We show that high quality ribbons and rings can be made using this technique. We also report on progress towards high mobility graphene monolayers on silicon carbide for device applications.

cond-mat.mes-hall↗

arXiv2007

Exchangeable partitions derived from Markovian coalescents with simultaneous multiple collisions

Kingman derived the Ewens sampling formula for random partitions from the genealogy model defined by a Poisson process of mutations along lines of descent governed by a simple coalescent process. Möhle described the recursion which determines the generalization of the Ewens sampling formula when the lines of descent are governed by a coalescent with multiple collisions. In a recent work by Dong, Gnedin and Pitman, authors exploit an analogy with the theory of regenerative composition and partition structures, and provide various characterizations of the associated exchangeable random partitions. This paper gives parallel results for the further generalized model with lines of descent following a coalescent with simultaneous multiple collisions.

math.PR↗

arXiv2007

Coagulation--fragmentation duality, Poisson--Dirichlet distributions and random recursive trees

In this paper we give a new example of duality between fragmentation and coagulation operators. Consider the space of partitions of mass (i.e., decreasing sequences of nonnegative real numbers whose sum is 1) and the two-parameter family of Poisson--Dirichlet distributions $\operatorname {PD}(α,θ)$ that take values in this space. We introduce families of random fragmentation and coagulation operators $\mathrm {Frag}_α$ and $\mathrm {Coag}_{α,θ}$, respectively, with the following property: if the input to $\mathrm {Frag}_α$ has $\operatorname {PD}(α,θ)$ distribution, then the output has $\operatorname {PD}(α,θ+1)$ distribution, while the reverse is true for $\mathrm {Coag}_{α,θ}$. This result may be proved using a subordinator representation and it provides a companion set of relations to those of Pitman between $\operatorname {PD}(α,θ)$ and $\operatorname {PD}(αβ,θ)$. Repeated application of the $\mathrm {Frag}_α$ operators gives rise to a family of fragmentation chains. We show that these Markov chains can be encoded naturally by certain random recursive trees, and use this representation to give an alternative and more concrete proof of the coagulation--fragmentation duality.

math.PR↗

arXiv2006

Exchangeable partitions derived from Markovian coalescents

Kingman derived the Ewens sampling formula for random partitions describing the genetic variation in a neutral mutation model defined by a Poisson process of mutations along lines of descent governed by a simple coalescent process, and observed that similar methods could be applied to more complex models. M{ö}hle described the recursion which determines the generalization of the Ewens sampling formula in the situation when the lines of descent are governed by a $Λ$-coalescent, which allows multiple mergers. Here we show that the basic integral representation of transition rates for the $Λ$-coalescent is forced by sampling consistency under more general assumptions on the coalescent process. Exploiting an analogy with the theory of regenerative partition structures, we provide various characterizations of the associated partition structures in terms of discrete-time Markov chains.

math.PR↗