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pro vyhledávání: '"Basak, Anirban"'
Fixing $\beta \ge 0$ and an integer $q \ge 2$, consider the ferromagnetic $q$-Potts measures $\mu_n^{\beta,B}$ on finite graphs ${\sf G}_n$ on $n$ vertices, with external field strength $B \ge 0$ and the corresponding random cluster measures $\varphi
Externí odkaz:
http://arxiv.org/abs/2312.16008
Autor:
Augeri, Fanny, Basak, Anirban
Consider a random symmetric matrix with i.i.d.~entries on and above its diagonal that are products of Bernoulli random variables and random variables with sub-Gaussian tails. Such a matrix will be called a sparse Wigner matrix and can be viewed as th
Externí odkaz:
http://arxiv.org/abs/2304.13364
Autor:
Banerjee, Sagnik, Jana, Koustav, Basak, Anirban, Fuhrer, Michael S, Culcer, Dimitrie, Muralidharan, Bhaskaran
The topological quantum field-effect transition in buckled 2D-Xenes can potentially be engineered to enable sub-thermionic transistor operation coupled with dissipationless ON-state conduction. Substantive device design strategies to harness this wil
Externí odkaz:
http://arxiv.org/abs/2202.12044
We analyze the electric field driven topological field effect transition on 2D-xene materials with the addition of momentum relaxation effects, in order to account for dephasing processes. The topological field effect transition between the quantum s
Externí odkaz:
http://arxiv.org/abs/2110.07287
Autor:
Basak, Anirban
We consider an Erd\H{o}s-R\'{e}nyi graph $\mathbb{G}(n,p)$ on $n$ vertices with edge probability $p$ such that \[ \sqrt{\frac{\log n}{\log \log n}} \ll np \le n^{1/2-o(1)}, \label{eq:abs} \tag{$\dagger$} \] and derive the upper tail large deviations
Externí odkaz:
http://arxiv.org/abs/2109.06242
Publikováno v:
Prob. Math. Phys. 4 (2023) 477-607
We prove localization with high probability on sets of size of order $N/\log N$ for the eigenvectors of non-Hermitian finitely banded $N\times N$ Toeplitz matrices $P_N$ subject to small random perturbations, in a very general setting. As perturbatio
Externí odkaz:
http://arxiv.org/abs/2103.17148
Autor:
Basak, Anirban, Basu, Riddhipratim
For a $\Delta$-regular connected graph ${\sf H}$ the problem of determining the upper tail large deviation for the number of copies of ${\sf H}$ in $\mathbb{G}(n,p)$, an Erd\H{o}s-R\'{e}nyi graph on $n$ vertices with edge probability $p$, has generat
Externí odkaz:
http://arxiv.org/abs/1912.11410
Autor:
Basak, Anirban, Zeitouni, Ofer
Consider an $N\times N$ Toeplitz matrix $T_N$ with symbol ${a }(\lambda) := \sum_{\ell=-d_2}^{d_1} a_\ell \lambda^\ell$, perturbed by an additive noise matrix $N^{-\gamma} E_N$, where the entries of $E_N$ are centered i.i.d.~random variables of unit
Externí odkaz:
http://arxiv.org/abs/1905.10244
Let $T_N$ denote an $N\times N$ Toeplitz matrix with finite, $N$ independent symbol ${\bf a}$. For $E_N$ a noise matrix satisfying mild assumptions (ensuring, in particular, that $N^{-1/2}\|E_N\|_{{\rm HS}}\to_{N\to\infty} 0$ at a polynomial rate), w
Externí odkaz:
http://arxiv.org/abs/1812.06207
Autor:
Basak, Anirban, Rudelson, Mark
We consider three different models of sparse random graphs:~undirected and directed Erd\H{o}s-R\'{e}nyi graphs, and random bipartite graph with an equal number of left and right vertices. For such graphs we show that if the edge connectivity probabil
Externí odkaz:
http://arxiv.org/abs/1809.08454