Lah distribution: Stirling numbers, records on compositions, and convex hulls of high-dimensional random walks
DOI10.1007/s00440-022-01146-9OpenAlexW3165070105WikidataQ114229356 ScholiaQ114229356MaRDI QIDQ2099818
Alexander Marynych, Zakhar Kabluchko
Publication date: 18 November 2022
Published in: Probability Theory and Related Fields (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2105.11365
random walksStirling numberscentral limit theoremlarge deviationsrecordsconvex hullsthreshold phenomenarandom polytopesWeyl chambersLambert \(W\)-functionmod-Poisson convergencerandom compositions\(f\)-vectorsneighborlinessconic intrinsic volumeslah distributionlah numbers
Geometric probability and stochastic geometry (60D05) Partitions of sets (05A18) Bell and Stirling numbers (11B73) Combinatorial probability (60C05) Asymptotic enumeration (05A16) Random convex sets and integral geometry (aspects of convex geometry) (52A22) Exponential and trigonometric functions (33B10) Limit theorems in probability theory (60Fxx)
Related Items
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Central limit theorems, Lee-Yang zeros, and graph-counting polynomials
- The least common multiple of random sets of positive integers
- Gaussian phase transitions and conic intrinsic volumes: steining the Steiner formula
- Stirling numbers of the second kind
- A dozen de Finetti-style results in search of a theory
- Limit theorems in the problem of distributing identical particles in different cells
- Log-concavity of Stirling numbers and unimodality of Stirling distributions
- Two conditional limit theorems with applications
- Regular simplices and Gaussian samples
- General Edgeworth expansions with applications to profiles of random trees
- Asymptotics of the uniform measure on simplices, and random compositions and partitions.
- Negative association of random variables, with applications
- Threshold phenomena for random cones
- Positive hulls of random walks and bridges
- Counting the faces of randomly-projected hypercubes and orthants, with applications
- Convex hulls of random walks, hyperplane arrangements, and Weyl chambers
- Intrinsic volumes of polyhedral cones: a combinatorial perspective
- Convex hulls of random walks: expected number of faces and face probabilities
- Mod-discrete expansions
- High-dimensional centrally symmetric polytopes with neighborliness proportional to dimension
- Angle sums of Schläfli orthoschemes
- Mod-Gaussian Convergence and Its Applications for Models of Statistical Mechanics
- Mod-ϕ Convergence
- The Lah Numbers and thenth Derivative of e1/x
- Mod‐Gaussian convergence and the value distribution of ζ(½ + it ) and related quantities
- Mode and Edgeworth expansion for the Ewens distribution and the Stirling numbers
- Mod-Gaussian convergence: new limit theorems in probability and number theory
- Mod-Poisson Convergence in Probability and Number Theory
- Counting faces of randomly projected polytopes when the projection radically lowers dimension
- Asymptotic Development of the Stirling Numbers of the First Kind
- Recent progress in coalescent theory
- Stochastic and Integral Geometry
- Observed universality of phase transitions in high-dimensional geometry, with implications for modern data analysis and signal processing
- An asymptotic estimate of the average number of steps of the parametric simplex method
- On the random coverage of the circle: a discrete model
- A unified approach to limit theorems for urn models
- Convex Polytopes
- On asymptotic expansions of Stirling numbers of the first and second kinds
- The on-line encyclopedia of integer sequences
- Probabilistic Methods in Combinatorial Analysis
- Another Look at Threshold Phenomena for Random Cones
- Living on the edge: phase transitions in convex programs with random data
- Limit theorems for the least common multiple of a random set of integers
- Mod- Convergence
- Asymptotics of the Stirling numbers of the second kind revisited
- Exponential Bounds Implying Construction of Compressed Sensing Matrices, Error-Correcting Codes, and Neighborly Polytopes by Random Sampling
- Sparse nonnegative solution of underdetermined linear equations by linear programming
- Neighborliness of randomly projected simplices in high dimensions
- Stirling Behavior is Asymptotically Normal
- Projections and angle sums of belt polytopes and permutohedra
- A theory of capacity and sparse neural encoding
