46 citations · 224 across the 39 of their papers we have counts for
34 papers · 1 filter
Markovian Random Words, a Gaussian Random Matrix Model and Beyond
Christian Houdré, Dorian Kidonakis
After centering and scaling, the length of the longest weakly increasing subsequence of a finite-state Markov random word converges to a Brownian last-passage functional with depen…
Normal approximation for functions of hidden Markov models
Christian Houdré, George Kerchev
The generalized perturbative approach is an all purpose variant of Stein's method used to obtain rates of normal approximation. Originally developed for functions of independent ra…
On Stein's Method for Multivariate Self-Decomposable Laws
Benjamin Arras, Christian Houdré
This work explores and develops elements of Stein's method of approximation, in the infinitely divisible setting, and its connections to functional analysis. It is mainly concerned…
On the limiting law of the length of the longest common and increasing subsequences in random words with arbitrary distributions
Clément Deslandes, Christian Houdré
Let and be two independent sequences of i.i.d. random variables, with values in a finite and totally ordered alphabet $\mathcal{A}_m:=\{1,\dots,…
Power Lower Bounds for the Central Moments of the Last Passage Time for Directed Percolation in a Thin Rectangle
Christian Houdré, Chen Xu
In directed last passage site percolation with i.i.d.~random weights with finite support over a grid, we prove that for large enough, the order of t…
On the Variance of the Length of the Longest Common Subsequences in Random Words With an Omitted Letter
Christian Houdré, Qingqing Liu
We investigate the variance of the length of the longest common subsequences of two independent random words of size , where the letters of one word are i.i.d. uniformly drawn f…
Lower bounds for fluctuations in first-passage percolation for general distributions
Michael Damron, Jack Hanson, Christian Houdré +1
In first-passage percolation (FPP), one assigns i.i.d.~weights to the edges of the cubic lattice and analyzes the induced weighted graph metric. If is the d…
On Stein's Method for Multivariate Self-Decomposable Laws With Finite First Moment
Benjamin Arras, Christian Houdré
We develop a multidimensional Stein methodology for non-degenerate self-decomposable random vectors in having finite first moment. Building on previous univariate fi…
On Stein's Method for Infinitely Divisible Laws With Finite First Moment
Benjamin Arras, Christian Houdré
We present, in a unified way, a Stein methodology for infinitely divisible laws (without Gaussian component) having finite first moment. Based on a correlation representation, we o…
On a Generalization of the Arcsine Law
Christian Houdré, Trevis J. Litherland
The gaps between the times, in a Weyl chamber, at which the sum of the increments of independent Brownian motions attains its maximum has a Dirichlet distribution.
Simulations, Computations, and Statistics for Longest Common Subsequences
Qingqing Liu, Christian Houdré
The length of the longest common subsequences (LCSs) is often used as a similarity measurement to compare two (or more) random words. Below we study its statistical behavior in mea…
Concentration of Geodesics in Directed Bernoulli Percolation
Christian Houdré, Chen Xu
For directed Bernoulli last passage percolation with i.i.d.~weights on vertices over a grid and for large enough, the geodesics are shown to be concentrated in a cy…
A Central Limit Theorem for the Optimal Alignments Score in Multiple Random Words
Ruoting Gong, Christian Houdré, Ümit Işlak
Let , where , , be independent sequences of independent a…
On the limiting law of the length of the longest common and increasing subsequences in random words
Jean-Christophe Breton, Christian Houdré
Let and be two sequences of independent and identically distributed (iid) random variables taking their values, uniformly, in a common totally…
A Central Limit Theorem for the Length of the Longest Common Subsequences in Random Words
Christian Houdré, Ümit Işlak
Let and be two independent sequences of independent identically distributed random variables taking their values in a common finite alphabet and…
GUE minors, maximal Brownian functionals and longest increasing subsequences
Florent Benaych-Georges, Christian Houdré
We present equalities in law between the spectra of the minors of a GUE matrix and some maximal functionals of independent Brownian motions. In turn, these results allow to recover…
On the Order of the Central Moments of the Length of the Longest Common Subsequences in Random Words
Christian Houdré, Jinyong Ma
We investigate the order of the -th, , central moment of the length of the longest common subsequence of two independent random words of size whose letters…
Sparse long blocks and the variance of the longest common subsequences in random words
S. Amsalu, C. Houdré, H. Matzinger
Consider two independent random strings having same length and taking values uniformly in a common finite alphabet. We study the order of the variance of the length of the longest…
On the Limiting Shape of Young Diagrams Associated With Markov Random Words
Christian Houdré, Trevis J. Litherland
Let be an irreducible, aperiodic, homogeneous Markov chain, with state space a totally ordered finite alphabet of size . Using combinatorial constructions and…
Asymptotics for the Length of the Longest Increasing Subsequence of Binary Markov Random Word
Christian Houdré, Trevis J. Litherland
Let be an irreducible, aperiodic, and homogeneous binary Markov chain and let be the length of the longest (weakly) increasing subsequence of $(X_k)_{1\le k…
Simultaneous large deviations for the shape of Young diagrams associated with random words
Christian Houdré, Jinyong Ma
We investigate the large deviations of the shape of the random RSK Young diagrams associated with a random word of size whose letters are independently drawn from an alphabet o…
On the rate of approximation in finite-alphabet longest increasing subsequence problems
Christian Houdré, Zsolt Talata
The rate of convergence of the distribution of the length of the longest increasing subsequence, toward the maximal eigenvalue of certain matrix ensembles, is investigated. For fin…
A Viscosity Approach to a Stochastic Control Problem on a Bounded Domain
Ruoting Gong, Christian Houdré
We study a stochastic control problem on a bounded domain, which arises from a continuous-time optimal management model. Via the corresponding Hamilton-Jacobi-Bellman equation the…
On the Limiting Shape of Young Tableaux Associated With Inhomogeneous Random Words
Christian Houdré, Hua Xu
The limiting shape of the random Young diagrams associated with an inhomogeneous random word is identified as a multidimensional Brownian functional. This functional is identical i…