53 citations · 489 across the 66 of their papers we have counts for
73 papers
On the finiteness of the group associated with weighted walks in multidimensional orthants
Andrew Elvey Price, Emmanuel Humbert, Kilian Raschel
In the study of walks with small steps confined to multidimensional orthants, a certain group of transformations plays a central role. In particular, several techniques to potentia…
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…
Singular walks in the quarter plane and Bernoulli numbers
Alin Bostan, Lucia Di Vizio, Kilian Raschel
We consider singular (aka genus ) walks in the quarter plane and their associated generating functions , which enumerate the walks starting from the origin, of fixed e…
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…
Enumeration of weighted quadrant walks: criteria for algebraicity and D-finiteness
Thomas Dreyfus, Andrew Elvey Price, Kilian Raschel
In the field of enumeration of weighted walks confined to the quarter plane, it is known that the generating functions behave very differently depending on the chosen step set; in…
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…
Elephant polynomials
Hélène Guérin, Lucile Laulin, Kilian Raschel
In this note, we study a family of polynomials that appear naturally when analysing the characteristic functions of the one-dimensional elephant random walk. These polynomials depe…
Logarithmic terms in discrete heat kernel expansions in the quadrant
Andrew Elvey-Price, Andreas Nessmann, Kilian Raschel
In the context of lattice walk enumeration in cones, we consider the number of walks in the quarter plane with fixed starting and ending points, prescribed step-set and given lengt…
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…
Intervals in the greedy Tamari posets
Mireille Bousquet-Mélou, Frédéric Chapoton
We consider a greedy version of the -Tamari order defined on -Dyck paths, recently introduced by Dermenjian. Inspired by intriguing connections between intervals in the ordin…
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…
Lattice walks confined to an octant in dimension 3: (non-)rationality of the second critical exponent
Luc Hillairet, Helen Jenne, Kilian Raschel
In the field of enumeration of walks in cones, it is known how to compute asymptotically the number of excursions (finite paths in the cone with fixed length, starting and ending p…