## 7 Citations

### Simulation of reflected Brownian motion on two dimensional wedges

- MathematicsStochastic Processes and their Applications
- 2022

### Reflected Brownian motion in a wedge: sum-of-exponential stationary densities

- Mathematics
- 2007

We give necessary and sufficient conditions for the stationary density of semimartingale reflected Brownian motion in a wedge to be written as a finite sum of terms of exponential product form.…

### Monte Carlo study of the hull distribution for the q = 1 Brauer model

- Mathematics, Physics
- 2006

We study a special case of the Brauer model in which every path of the model has weight q = 1. The model has been studied before as a solvable lattice model and can be viewed as a Lorentz lattice…

### Diamond aggregation

- MathematicsMathematical Proceedings of the Cambridge Philosophical Society
- 2010

Abstract Internal diffusion-limited aggregation is a growth model based on random walk in ℤd. We study how the shape of the aggregate depends on the law of the underlying walk, focusing on a family…

### Green’s Functions with Oblique Neumann Boundary Conditions in the Quadrant

- MathematicsJournal of Theoretical Probability
- 2020

We study semi-martingale obliquely reflected Brownian motion with drift in the first quadrant of the plane in the transient case. Our main result determines a general explicit integral expression for…

### Rotor-Router Aggregation on the Layered Square Lattice

- MathematicsElectron. J. Comb.
- 2010

It is shown that for a certain choice of initial rotors, the occupied cluster of occupied sites grows as a perfect diamond.

### Green's functions with oblique Neumann boundary conditions in a wedge

- Mathematics
- 2019

We study semi-martingale obliquely reflected Brownian motion (SRBM) with drift in a wedge of the plane in the transient case. Our main result determines a general explicit integral expression for the…

## References

SHOWING 1-10 OF 18 REFERENCES

### Brownian motion in a wedge with oblique reflection at the boundary

- Mathematics
- 1983

This work is concerned with the existence and uniqueness of a strong Markov process that has continuous sample paths and the following additional properties:
(i)
The state space is an infinite…

### Random planar curves and Schramm-Loewner evolutions

- Geology
- 2003

We review some of the results that have been derived in the last years on conformal invariance, scaling limits and properties of some two-dimensional random curves. In particular, we describe the…

### Conformal restriction: The chordal case

- Mathematics
- 2003

We characterize and describe all random subsets K of a given simply connected planar domain (the upper half-plane Η, say) which satisfy the conformal restriction” property, i.e., K connects two fixed…

### Intersection Exponents for Planar Brownian Motion

- Mathematics
- 1999

We derive properties concerning all intersection exponents for planar Brownian motion and we define generalized exponents that, loosely speaking, correspond to noninteger numbers of Brownian paths.…

### Critical Exponents, Conformal Invariance and Planar Brownian Motion

- Mathematics
- 2001

In this review paper, we first discuss some open problems related to two-dimensional self-avoiding paths and critical percolation. We then review some closely related results (joint work with Greg…

### SLE and Triangles

- Mathematics
- 2002

By analogy with Carleson's observation on Cardy's formula describing crossing probabilities for the scaling limit of critical percolation, we exhibit ``privileged geometries'' for Stochastic Loewner…

### Values of Brownian intersection exponents, I: Half-plane exponents

- Physics
- 1999

Theoretical physics predicts that conformal invariance plays a crucial role in the macroscopic behavior of a wide class of two-dimensional models in statistical physics (see, e.g., [4], [6]). For…

### Excursion decompositions for SLE and Watts' crossing formula

- Mathematics
- 2004

It is known that Schramm-Loewner Evolutions (SLEs) have a.s. frontier points if κ>4 and a.s. cutpoints if 4<κ<8. If κ>4, an appropriate version of SLE(κ) has a renewal property: it starts afresh…

### Beta-gamma random variables and intertwining relations between certain Markov processes

- Mathematics
- 1998

In this paper, we study particular examples of the intertwining relation
Qt? = ?Pt
between two Markov semi-groups (Pt, t = 0) defined respectively on (E,e) and (F,F), via the Markov kernel
?: (E,e) ?…