Related papers: The dinner table problem: the rectangular case

Consider the problem \begin{eqnarray*} -\Delta u &=& v^{\frac 2{N-2}},\quad v>0\quad {in}\quad \Omega, -\Delta v &=& u^{p},\:\:\:\quad u>0\quad {in}\quad \Omega, u&=&v\:\:=\:\:0 \quad {on}\quad \partial \Omega, \end{eqnarray*} where…

We study the joint asymptotics of forward and backward processes of numbers of non-empty urns in an infinite urn scheme. The probabilities of balls hitting the urns are assumed to satisfy the conditions of regular decrease. We prove weak…

We consider non-negative solutions of the fast diffusion equation $u_t=\Delta u^m$ with $m \in (0,1)$, in the Euclidean space R^d, d?3, and study the asymptotic behavior of a natural class of solutions, in the limit corresponding to…

We consider the semilinear Lane-Emden problem in a smooth bounded domain of the plane. The aim of the paper is to analyze the asymptotic behavior of sign changing solutions as the exponent p of the nonlinearity goes to infinity. Among other…

We study the random binary contingency tables with non-uniform margin. More precisely, for parameters $n,\delta,B,C$, we consider $X=(X_{ij})$ with $X_{ij}\in \lbrace 0,1\rbrace$, the random binary contingency tables whose first…

Let T(m,n) denote the number of ways to tile an m-by-n rectangle with dominos. For any fixed m, the numbers T(m,n) satisfy a linear recurrence relation, and so may be extrapolated to negative values of n; these extrapolated values satisfy…

We consider the large-$N$ asymptotics of a system of discrete orthogonal polynomials on an infinite regular lattice of mesh $\frac{1}{N}$, with weight $e^{-NV(x)}$, where $V(x)$ is a real analytic function with sufficient growth at…

For a given blocklength we determine the number of interleavers which have spread equal to two. Using this, we find out the probability that a randomly chosen interleaver has spread two. We show that as blocklength increases, this…

Let $s$ be the sum-of-digits function in base $2$, which returns the number of $\mathtt 1$s in the base-2 expansion of a nonnegative integer. For a nonnegative integer $t$, define the asymptotic density \[ c_t=\lim_{N\rightarrow \infty}…

Suppose you and your friend both do $n$ tosses of an unfair coin with probability of heads equal to $\alpha$. What is the behavior of the probability that you obtain at least $d$ more heads than your friend if you make $r$ additional…

Let $S_r(p,q)$ be the $r$-associated Stirling numbers of the second kind, the number of ways to partition a set of size $p$ into $q$ subsets of size at least $r$. For $r=1$, these are the standard Stirling numbers of the second kind, and…

We analyze a stochastic particle system of 5 neighbors. Considering eigenvalue problem of transition matrix, we propose a conjecture that asymptotic distribution of the system is determined by the number of specific local patterns in the…

We describe the limit (for two topologies) of large uniform random square permutations, i.e., permutations where every point is a record. The starting point for all our results is a sampling procedure for asymptotically uniform square…

We consider the asymptotic behaviour of positive solutions u of the conformal scalar curvature equation, \Delta u + n(n-2)/4 u^{(n+2)(n-2) = 0, in the neighbourhood of isolated singularities in the standard Euclidean ball. Although…

We prove specific biases in the number of occurrences of parts belonging to two different residue classes $a$ and $b$, modulo a fixed non-negative integer $m$, for the sets of unrestricted partitions, partitions into distinct parts, and…

We have developed a continuous model of indirect reciprocity and thereby investigated effects of mutation in assessment rules. Within this continuous framework, the difference between the resident and mutant norms is treated as a small…

We describe the asymptotic behaviour and the stability properties of the solutions to a second order rational difference equation.

In this paper, we consider the asymptotic behavior of positive solutions of the biharmonic equation $$ \Delta^2 u = u^p~~~~~~~in ~ B_1 \backslash \{0\}$$ with an isolated singularity, where the punctured ball $B_1 \backslash \{0\} \subset…

The paper studies asymptotic behavior of the loss probability for the $GI/M/m/n$ queueing system as $n$ increases to infinity. The approach of the paper is based on applications of classic results of Tak\'acs (1967) and the Tauberian…

We discuss the conditions under which identical particles may yet be distinguishable and the relationship between particle permutation and exchange. We show that we can always define permutation-symmetric state vectors. When the particles…