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Creators/Authors contains: "Chakraborty, Suman"

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  1. ; ; (, Journal of Applied Probability)
    Abstract We determine the order of thek-core in a large class of dense graph sequences. Let$$G_n$$be a sequence of undirected,n-vertex graphs with edge weights$$\{a^n_{i,j}\}_{i,j \in [n]}$$that converges to a graphon$$W\colon[0,1]^2 \to [0,+\infty)$$in the cut metric. Keeping an edge (i,j) of$$G_n$$with probability$${a^n_{i,j}}/{n}$$independently, we obtain a sequence of random graphs$$G_n({1}/{n})$$. Using a branching process and the theory of dense graph limits, under mild assumptions we obtain the order of thek-core of random graphs$$G_n({1}/{n})$$. Our result can also be used to obtain the threshold of appearance of ak-core of ordern. 
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    Free, publicly-accessible full text available March 1, 2026
  2. ; ; (, The Annals of Applied Probability)
    We consider heterogeneously interacting diffusive particle systems and their large population limit. The interaction is of mean field type with weights characterized by an underlying graphon. A law of large numbers result is established as the system size increases and the underlying graphons converge. The limit is given by a graphon mean field system consisting of independent but heterogeneous nonlinear diffusions whose probability distributions are fully coupled. Well-posedness, continuity and stability of such systems are provided. We also consider a not-so-dense analogue of the finite particle system, obtained by percolation with vanishing rates and suitable scaling of interactions. A law of large numbers result is proved for the convergence of such systems to the corresponding graphon mean field system. 
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  3. ; ; ; ; ; ; ; ; (, Materials Horizons)
    Impurities in water affect ice adhesion strength on surfaces. Depending on the freezing rate, they can be trapped in ice or pushed out, forming a lubricating layer. They also affect the quasi-liquid layer between ice and surface, impacting adhesion. 
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  4. ; ; (, Journal of Statistical Physics)
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  5. ; (, The Electronic Journal of Combinatorics)
    A graph $$G$$ percolates in the $$K_{r,s}$$-bootstrap process if we can add all missing edges of $$G$$ in some order such that each edge creates a new copy of $$K_{r,s}$$, where $$K_{r,s}$$ is the complete bipartite graph. We study $$K_{r,s}$$-bootstrap percolation on the Erdős-Rényi random graph, and determine the percolation threshold for balanced $$K_{r,s}$$ up to a logarithmic factor. This partially answers a question raised by Balogh, Bollobás, and Morris. We also establish a general lower bound of the percolation threshold for all $$K_{r,s}$$, with $$r\geq s \geq 3$$. 
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  6. ; ; ; ; (, Physical Review E)
    null (Ed.)
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