Lucas Teyssier
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View article: Every cutoff profile is possible
Every cutoff profile is possible Open
We introduce fruit-inosculated-tree Markov chains. These chains have easily tunable parameters and are a good source of examples. In particular, we prove that every cutoff profile is possible, with any cutoff time and window size.
View article: Bounds on skew dimensions and characters of symmetric groups via thick hook decompositions
Bounds on skew dimensions and characters of symmetric groups via thick hook decompositions Open
We bound the number of standard tableaux of skew shapes via thick hook decompositions in the Naruse hook length formula. Combining this with elementary counting arguments in the Murnaghan--Nakayama rule, we establish a uniform bound on cha…
View article: Characters of symmetric groups: sharp bounds on virtual degrees and the Witten zeta function
Characters of symmetric groups: sharp bounds on virtual degrees and the Witten zeta function Open
We prove sharp bounds on the virtual degrees introduced by Larsen and Shalev. This leads to improved bounds on characters of symmetric groups. We then sharpen bounds of Liebeck and Shalev concerning the Witten zeta function. Our main appli…
View article: On the universality of fluctuations for the cover time
On the universality of fluctuations for the cover time Open
We consider random walks on finite vertex-transitive graphs $Γ$ of bounded degree. We find a simple geometric condition which characterises the cover time fluctuations: the suitably normalised cover time converges to a standard Gumbel vari…
View article: Cutoff profiles for quantum Lévy processes and quantum random transpositions
Cutoff profiles for quantum Lévy processes and quantum random transpositions Open
We consider a natural analogue of Brownian motion on free orthogonal quantum groups and prove that it exhibits a cutoff at time $N\ln(N)$. Then, we study the induced classical process on the real line and compute its atoms and density. Thi…
View article: Limit profile for random transpositions
Limit profile for random transpositions Open
We present an improved version of Diaconis–Shahshahani upper bound lemma, which is used to compute the limiting value of the distance to stationarity. We then apply it to the random transposition shuffle.
View article: Limit profile for random transpositions
Limit profile for random transpositions Open
We present an improved version of Diaconis' upper bound lemma, which is used to compute the limiting value of the distance to stationarity. We then apply it to random transpositions studied by Diaconis and Shahshahani.