Partial balayage on Riemannian manifolds

Gustafsson, Björn; Roos, Joakim

doi:10.1016/j.matpur.2017.07.013

Cited by 15 publications

(9 citation statements)

References 39 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For the above example it turns out that the total mass M R on the boundary tends to zero as R → ∞. In fact, in [3] it is shown that the boundary mass vanishes in general in dimension d = 2. As already mentioned in Section 2.2, in [12] it is shown that one can define a partial balayage operation Bal(σ, 0) (see Definition 2.8), in some sense corresponding to letting R be R = ∞ in Definition 2.3.…”

Section: Boundary Properties For Large Confining Radiimentioning

confidence: 85%

See 1 more Smart Citation

Partial Balayage and a Generalization of the Divisible Sandpile Model

Roos

2016

Preprint

Self Cite

View full text Add to dashboard Cite

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 limit as the lattice spacing tends to zero, if they are started with the same initial mass configuration. It is straightforward to observe that this scaling limit is precisely the same as the potential-theoretic operation of taking the partial balayage of this initial mass configuration to the Lebesgue measure. However, from the theory of the partial balayage operation it is clear that one may take the partial balayage of a mass configuration to a more general measure than the Lebesgue measure, which one cannot do for the three aggregation models described by Levine and Peres. In this paper we therefore generalize one of these models, the divisible sandpile model, in mainly a bounded setting, and show that a natural scaling limit of this generalization is given by a general partial balayage operation.

show abstract

Section: Boundary Properties For Large Confining Radiimentioning

confidence: 85%

“…However, there does not seem to be any reason for such a result to hold in general, at least not for dimensions d ≥ 3. In the upcoming paper [3] the example Bal R (σ, 0) is treated in detail, where σ is the measure…”

mentioning

confidence: 99%

Partial Balayage and a Generalization of the Divisible Sandpile Model

Roos

2016

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…e.g. [8] and [14]). By introducing a confinementparameter as above, one obtains more general ensembles with various restrictions near the boundary.…”

Section: Discussionmentioning

confidence: 99%

On boundary confinements for the Coulomb gas

Ameur,

Kang,

Seo

2019

Preprint

View full text Add to dashboard Cite

We introduce a family of boundary confinements for Coulomb gas ensembles, and study them in the two-dimensional determinantal case of random normal matrices. The family interpolates between the free boundary and hard edge cases, which have been well studied in various random matrix theories. The confinement can also be relaxed beyond the free boundary to produce ensembles with more fuzzy boundaries, i.e., where the particles are more and more likely to be found outside of the boundary. The resulting ensembles are investigated with respect to scaling limits and distribution of the maximum modulus. In particular, we prove existence of a new point field -a limit of scaling limits to the ultraweak point when the droplet ceases to be well-defined.

show abstract

“…To name just a few references which give a good background, we suggest [2,17,23,14], and their respective bibliographies. Connections between quadrature domains and the sphere appear from the realm of fluid dynamics in [9,10] and in the treatment of potential theory on manifolds in [25,16].…”

Section: Q(y)dµ(y)mentioning

confidence: 99%

“…We implement this for a particular case, and plot the results in Maple. Place point charges of intensity q = 41−3 √ 41 82 at the points (± 16 25 , 0, − 3 √ 41 25 ) of the unit sphere. Figure 1 shows the boundary of the resulting equilibrium support, together with the individual caps of influence.…”

Section: Examplesmentioning

confidence: 99%

Logarithmic Equilibrium on the Sphere in the Presence of Multiple Point Charges

Legg

Dragnev

2019

Preprint

View full text Add to dashboard Cite

With the sphere S 2 ⊂ R 3 as a conductor holding a unit charge with logarithmic interactions, we consider the problem of determining the support of the equilibrium measure in the presence of an external field consisting of finitely many point charges on the surface of the sphere. We determine that for any such configuration, the complement of the equilibrium support is the stereographic preimage from the plane of a union of classical quadrature domains, whose orders sum to the number of point charges.

show abstract

Partial balayage on Riemannian manifolds

Cited by 15 publications

References 39 publications

Partial Balayage and a Generalization of the Divisible Sandpile Model

Partial Balayage and a Generalization of the Divisible Sandpile Model

On boundary confinements for the Coulomb gas

Logarithmic Equilibrium on the Sphere in the Presence of Multiple Point Charges

Contact Info

Product

Resources

About