53 citations · 489 across the 66 of their papers we have counts for
47 papers · 1 filter
Persistence probabilities of MA(1) sequences with Laplace innovations and -deformed zigzag numbers
Frank Aurzada, Kilian Raschel
We study the persistence probabilities of a moving average process of order one with innovations that follow a Laplace distribution. The persistence probabilities can be computed f…
Asymptotics of returns to the coordinate axes for conditioned planar simple random walks
Rodolphe Garbit, Kilian Raschel
In this paper we study the number of returns to the coordinate axes for two-dimensional nearest-neighbour random walks. While one-dimensional results on returns are classical, much…
Boundary contacts for reflected random walks in the quarter plane
Viet Hung Hoang, Kilian Raschel
We investigate reflected random walks in the quarter plane, with particular emphasis on the time spent along the reflection boundary axes. Assuming the drift of the random walk lie…
Persistence probabilities for MA(1) sequences with uniform innovations
Frank Aurzada, Kilian Raschel
We study the persistence probabilities of a moving average process of order one with uniform innovations. We identify a number of regions-characterized by the location of the unifo…
Discrete harmonic polynomials in multidimensional orthants
Emmanuel Humbert, Kilian Raschel
We consider multidimensional random walks in pyramidal cones (or multidimensional orthants), which are intersections of a finite number of half-spaces. We explore the connection be…
Limit shape of the leaky Abelian sandpile model with multiple layers
Théo Ballu, Cédric Boutillier, Sevak Mkrtchyan +1
In this paper we study a triple generalization of the Leaky Abelian Sandpile Model (LASM) of Alevy and Mkrtchyan, originally analyzed in the case of the square lattice in dimension…
Enumeration of walks in multidimensional orthants and reflection groups
Léa Gohier, Emmanuel Humbert, Kilian Raschel
We consider (random) walks in a multidimensional orthant. Using the idea of universality in probability theory, one can associate a unique polyhedral domain to any given walk model…
On the first hitting time of a high-dimensional orthant
Emmanuel Humbert, Kilian Raschel
We consider a collection of independent standard Brownian particles (or random walks), starting from a configuration where at least one particle is positive, and study the first ti…
On the limit law of the superdiffusive elephant random walk
Hélène Guérin, Lucile Laulin, Kilian Raschel +1
When the memory parameter of the elephant random walk is above a critical threshold, the process becomes superdiffusive and, once suitably normalised, converges to a non-Gaussian r…
Invariant measure of gaps in degenerate competing three-particle systems
Sandro Franceschi, Tomoyuki Ichiba, Ioannis Karatzas +1
We study the gap processes in a degenerate system of three particles interacting through their ranks. We obtain the Laplace transform of the invariant measure of these gaps, and an…
A fixed-point equation approach for the superdiffusive elephant random walk
Hélène Guérin, Lucile Laulin, Kilian Raschel
We study the elephant random walk in arbitrary dimension . Our main focus is the limiting random variable appearing in the superdiffusive regime. Building on a link betwee…
Random Walks in the High-Dimensional Limit II: The Crinkled Subordinator
Zakhar Kabluchko, Alexander Marynych, Kilian Raschel
A crinkled subordinator is an -valued random process which can be thought of as a version of the usual one-dimensional subordinator with each out of countably many jumps be…
Multivariate multiplicative functions of uniform random vectors in large integer domains
Zakhar Kabluchko, Oleksandr Marynych, Kilian Raschel
For a wide class of sequences of integer domains , , we prove distributional limit theorems for , w…
Random walks with drift inside a pyramid: convergence rate for the survival probability
Rodolphe Garbit, Kilian Raschel
We consider multidimensional random walks in pyramids, which by definition are cones formed by finite intersections of half-spaces. The main object of interest is the survival prob…
Harmonic functions for singular quadrant walks
Viet Hung Hoang, Kilian Raschel, Pierre Tarrago
We consider discrete (time and space) random walks confined to the quarter plane, with jumps only in directions with and small negative jumps, i.e., $i,j \geq…
A dual skew symmetry for transient reflected Brownian motion in an orthant
Sandro Franceschi, Kilian Raschel
We introduce a transient reflected Brownian motion in a multidimensional orthant, which is either absorbed at the apex of the cone or escapes to infinity. We address the question o…
Stationary Brownian motion in a 3/4-plane: Reduction to a Riemann-Hilbert problem via Fourier transforms
Guy Fayolle, Sandro Franceschi, Kilian Raschel
The stationary reflected Brownian motion in a three-quarter plane has been rarely analyzed in the probabilistic literature, in comparison with the quarter plane analogue model. In…
Persistence for a class of order-one autoregressive processes and Mallows-Riordan polynomials
Gerold Alsmeyer, Alin Bostan, Kilian Raschel +1
We establish exact formulae for the persistence probabilities of an AR(1) sequence with symmetric uniform innovations in terms of certain families of polynomials, most notably a fa…
On the stationary distribution of reflected Brownian motion in a non-convex wedge
Guy Fayolle, Sandro Franceschi, Kilian Raschel
We study the stationary reflected Brownian motion in a non-convex wedge, which, compared to its convex analogue model, has been much rarely analyzed in the probabilistic literature…
On the stationary distribution of reflected Brownian motion in a wedge: differential properties
M. Bousquet-Mélou, A. Elvey Price, S. Franceschi +2
We consider the classical problem of determining the stationary distribution of the semimartingale reflected Brownian motion (SRBM) in a two-dimensional wedge. Under standard assum…
Reflected random walks and unstable Martin boundary
Irina Ignatiouk-Robert, Irina Kourkova, Kilian Raschel
We introduce a family of two-dimensional reflected random walks in the positive quadrant and study their Martin boundary. While the minimal boundary is systematically equal to a un…
Martin boundary of random walks in convex cones
Jetlir Duraj, Kilian Raschel, Pierre Tarrago +1
We determine the asymptotic behavior of the Green function for zero-drift random walks confined to multidimensional convex cones. As a consequence, we prove that there is a unique…
Martin boundary of killed random walks on isoradial graphs
Cédric Boutillier, Kilian Raschel
We consider killed planar random walks on isoradial graphs. Contrary to the lattice case, isoradial graphs are not translation invariant, do not admit any group structure and are s…
On the least common multiple of several random integers
Alin Bostan, Alexander Marynych, Kilian Raschel
Let denote the least common multiple of independent random integers uniformly chosen in . In this note, using a purely probabilistic approach, we de…