Abstract We introduce and study a one parameter deformation of the polynuclear growth (PNG) in (1+1)-dimensions, which we call $t$-PNG model. It is defined by requiring that, when two expanding islands merge, with probability $t$ they sprout another island on top merging location. At $t=0$, this becomes standard (non-deformed) PNG model droplet geometry, can be reformulated through longest incr...

El presente estudio pretende analizar cómo Marcel Prévost (1862-1941), escritor descrito como un “erótico cristiano”, muestra la variopinta forma que tenían las mujeres de entender religión. En él podrá constatarse no eran pocas damas burguesas satisfacían su libidinoso deseo en el mismo confesionario; ni tampoco menos número acudían a Iglesia para se eximiera sus pecados, pudiendo así, Afrodit...

In Group Synchronization, one attempts to find a collection of unknown group elements from noisy measurements of their pairwise differences. Several important problems in vision and data analysis reduce to group synchronization over various compact groups. Spectral Group Synchronization is a commonly used, robust algorithm for solving group synchronization problems, which relies on diagonalizat...

Abstract We study statistical and computational limits of clustering when the means centres are sparse their dimension is possibly much larger than sample size. Our theoretical analysis focuses on model $X_i=z_i \theta +\varepsilon _{i}, \ z_i \in \{-1,1\}, \varepsilon _i \thicksim \mathcal{N}(0, I)$, which has two clusters with $\theta $ $-\theta $. provide a finite new algorithm based Princip...

We study the properties of spin-less non-interacting fermions trapped in a confining potential one dimension but presence or more impurities which are modelled by delta function potentials. use method based on single particle Green's function. For impurity placed bulk, we compute density Fermi gas near impurity. Our results, addition to recovering Friedel oscillations at large distance from imp...

We study the statistical limits of both detecting and estimating a rank-one deformation of a symmetric random Gaussian tensor. We establish upper and lower bounds on the critical signal-to-noise ratio, under a variety of priors for the planted vector: (i) a uniformly sampled unit vector, (ii) i.i.d. ±1 entries, and (iii) a sparse vector where a constant fraction ρ of entries are i.i.d. ±1 and t...