Related papers: Dynamical Spin Limit Shape of Young Diagram and Sp…

The irreducible decomposition of successive restriction and induction of irreducible representations of a symmetric group gives rise to a Markov chain on Young diagrams keeping the Plancherel measure invariant. Starting from this Res-Ind…

We place model-independent constraints on theories of massive spin-2 particles by considering the positivity of the phase shift in eikonal scattering. The phase shift is an asymptotic $S$-matrix observable, related to the time delay/advance…

We study a discrete time multitype branching random walk on a finite space with finite set of types. Particles follow a Markov chain on the spatial space whereas offspring distributions are given by a random field that is fixed throughout…

The multiplicities of the decomposition of the product of an arbitrary number $n$ of spin $s$ states into irreducible $SU(2)$ representations are computed. Two complementary methods are presented, one based on random walks in representation…

The branching rule for the tower of wreath products of a finite group by the symmetric groups induces a stochastic process on the set of multiple Young diagrams through random transitions of boxes of the diagrams between one another. We…

We investigate the asymptotic in $N$ of the mixing times of a Markov dynamics on $N-1$ ordered particles in an interval. This dynamics consists in resampling at independent Poisson times each particle according to a probability measure on…

This paper studies Markov chains on the symmetric group $S_n$ where the transition probabilities are given by the Ewens distribution with parameter $\theta>1$. The eigenvalues are identified to be proportional to the content polynomials of…

Dynamics of Wilson loops in pure Yang-Mills theories is analyzed in terms of random walks of the holonomies of the gauge field on the gauge group manifold. It is shown that such random walks should necessarily be free. The distribution of…

We consider quantum graphs with spin-orbit couplings at the vertices. Time-reversal invariance implies that the bond S-matrix is in the orthogonal or symplectic symmetry class, depending on spin quantum number s being integer or…

Let $(X_n)_{n \ge 0}$ be an irreducible, aperiodic, homogeneous Markov chain, with state space a totally ordered finite alphabet of size $m$. Using combinatorial constructions and weak invariance principles, we obtain the limiting shape of…

We consider a matrix branching random walk on the semi-group of nonnegative matrices, where we are able to derive, under general assumptions, an analogue of Biggins' martingale convergence theorem for the additive martingale $W_n$, a spinal…

We consider, following the work of S. Kerov, random walks which are continuous-space generalizations of the Hook Walks defined by Greene-Nijenhuis-Wilf, performed under the graph of a continual Young diagram. The limiting point of these…

We show how mapping techniques inherent to $N^{2}$-dimensional discrete phase spaces can be used to treat a wide family of spin systems which exhibits squeezing and entanglement effects. This algebraic framework is then applied to the…

We study convergence to equilibrium for a large class of Markov chains in random environment. The chains are sparse in the sense that in every row of the transition matrix $P$ the mass is essentially concentrated on few entries. Moreover,…

We address the dynamics of a single spin embedded in the tunneling barrier between two superconductors. As a consequence of pair correlations in the superconducting state, the spin displays a rich and unusual dynamics. To properly describe…

We introduce a new family of integrable stochastic processes, called \textit{dynamical stochastic higher spin vertex models}, arising from fused representations of Felder's elliptic quantum group $E_{\tau, \eta} (\mathfrak{sl}_2)$. These…

In this paper, we obtain explicit branching laws for all irreducible unitary representations of $\Spin(N,1)$ restricted to a parabolic subgroup $P$. The restriction turns out to be a finite direct sum of irreducible unitary representations…

We explore the space of meromorphic amplitudes with extra constraints coming from the shape of the leading Regge trajectory. This information comes in two guises: it bounds the maximal spin of exchanged particles of a given mass; it leads…

We construct a renewal structure for random walks on surface groups. The renewal times are defined as times when the random walks enters a particular type of a cone and never leaves it again. As a consequence, the trajectory of the random…

We evaluate the limit distribution of the maximal excursion of a random walk in any dimension for homogeneous environments and for self-similar supports under the assumption of spherical symmetry. This distribution is obtained in closed…