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We first establish new local limit estimates for the probability that a nondecreasing integer-valued random walk lies at time $n$ at an arbitrary value, encompassing in particular large deviation regimes. This enables us to derive scaling…
The control of traffic signals is crucial for improving transportation efficiency. Recently, learning-based methods, especially Deep Reinforcement Learning (DRL), garnered substantial success in the quest for more efficient traffic signal…
Rapidly Exploring Random Trees (RRT) is one of the most widely used algorithms for motion planning in the field of robotics. To reduce the exploration time, RRT-Connect was introduced where two trees are simultaneously formed and eventually…
We prove a law of large numbers for the range of rotor walks with random initial configuration on regular trees and on Galton-Watson trees. More precisely, we show that on the classes of trees under consideration, even in the case when the…
We derive a message passing method for computing the spectra of locally tree-like networks and an approximation to it that allows us to compute closed-form expressions or fast numerical approximates for the spectral density of random graphs…
Consider a point particle moving through a Poisson distributed array of cubes all oriented along the axes - the random wind-tree model introduced in Ehrenfest-Ehrenfest (1912). We show that, in the joint Boltzmann-Grad and diffusive limit…
Continuous time branching models are used to create random fractals in a Euclidean space, whose Hausdorff dimension is controlled by an input parameter. Finite realizations are applied in modelling the set of sites visited in models of…
Tree-structured data naturally appear in various fields, particularly in biology where plants and blood vessels may be described by trees, but also in computer science because XML documents form a tree structure. This paper is devoted to…
Decision trees are widely used for non-linear modeling, as they capture interactions between predictors while producing inherently interpretable models. Despite their popularity, performing inference on the non-linear fit remains largely…
We generalize the classical single-crossing property to single-crossing property on trees and obtain new ways to construct Condorcet domains which are sets of linear orders which possess the property that every profile composed from those…
Trees of finite cone type have appeared in various contexts. In particular, they come up as simplified models of regular tessellations of the hyperbolic plane. The spectral theory of the associated Laplacians can thus be seen as induced by…
We consider random walks indexed by arbitrary finite random or deterministic trees. We derive a simple sufficient criterion which ensures that the maximal displacement of the tree-indexed random walk is determined by a single large jump.…
An asymmetric exclusion process type process, where cars move forward along a closed road that starts and terminates at a parking garage, displays dynamic phase transitions into two types of condensate phases where the garage becomes…
We investigate level-set percolation of the Gaussian free field on transient trees, for instance on super-critical Galton-Watson trees conditioned on non-extinction. Recently developed Dynkin-type isomorphism theorems provide a comparison…
Sorting is a foundational problem in computer science that is typically employed on sequences or total orders. More recently, a more general form of sorting on partially ordered sets (or posets), where some pairs of elements are…
We explore the tree limits recently defined by Elek and Tardos. In particular, we find tree limits for many classes of random trees. We give general theorems for three classes of conditional Galton-Watson trees and simply generated trees,…
We consider the preferential attachment model with location-based choice introduced by Haslegrave, Jordan and Yarrow as a model in which condensation phenomena can occur [Haslegrave et al. 2020]. In this model every vertex carries an…
We adapt ideas and concepts developed in optimal transport (and its martingale variant) to give a geometric description of optimal stopping times of Brownian motion subject to the constraint that the distribution of the stopping time is a…
We consider the randomly biased random walk on trees in the slow movement regime as in [HS16], whose potential is given by a branching random walk in the boundary case. We study the heavy range up to the $n$-th return to the root, i.e., the…
Designing fare systems for public transportation networks is a challenging task. A popular approach is to partition the network into fare zones (``zoning'') and fix journey prices depending on the number of traversed zones (``pricing''). In…